√3x+7=3x+5
How do I solve when the answer is -1?
Squaring both sides
3 x + 7 = ( 3 x + 5 ) ^ 2
3 x + 7 = 9 x ^ 2 + 2 * 3 x * 5 + 5 ^ 2
3 x + 7 = 9 x ^ 2 + 30 x + 25
0 = 9 x ^ 2 + 30 x + 25 - 3 x - 7
9 x ^ 2 + 27 x + 18 = 0 Divide both sides by 9
x ^ 2 + 3 x + 2 = 0
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To solve the equation √3x + 7 = 3x + 5 and find the value of x that results in an answer of -1, follow these steps:
Step 1: Start by isolating the radical term on one side of the equation. Subtract 7 from both sides:
√3x = 3x + 5 - 7
√3x = 3x - 2
Step 2: Square both sides of the equation to eliminate the radical:
(√3x)^2 = (3x - 2)^2
3x = (3x - 2)(3x - 2)
3x = 9x^2 - 12x + 4
Step 3: Rearrange the equation to bring all terms to one side:
9x^2 - 12x + 4 - 3x = 0
9x^2 - 15x + 4 = 0
Step 4: Factorize or use the quadratic formula to solve for x. Unfortunately, this equation does not factorize easily, so let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 9, b = -15, and c = 4. Substituting these values into the quadratic formula:
x = (-(-15) ± √((-15)^2 - 4(9)(4))) / (2(9))
x = (15 ± √(225 - 144)) / 18
x = (15 ± √81) / 18
Step 5: Simplify the expression:
x = (15 ± 9) / 18
Now we have two possible solutions:
(i) x = (15 + 9) / 18
(ii) x = (15 - 9) / 18
Solving each equation gives us:
(i) x = 24 / 18 = 4 / 3 ≈ 1.33
(ii) x = 6 / 18 = 1 / 3 ≈ 0.33
Therefore, there is no solution to the equation √3x + 7 = 3x + 5 where x equals -1.