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Simplifying 9x2 + -60x = 100 Reorder the terms: -60x + 9x2 = 100 Solving -60x + 9x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + -60x + 9x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -60x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -11.11111111 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '11.11111111' to each side of the equation. -11.11111111 + -6.666666667x + 11.11111111 + x2 = 0 + 11.11111111 Reorder the terms: -11.11111111 + 11.11111111 + -6.666666667x + x2 = 0 + 11.11111111 Combine like terms: -11.11111111 + 11.11111111 = 0.00000000 0.00000000 + -6.666666667x + x2 = 0 + 11.11111111 -6.666666667x + x2 = 0 + 11.11111111 Combine like terms: 0 + 11.11111111 = 11.11111111 -6.666666667x + x2 = 11.11111111 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = 11.11111111 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 11.11111111 + 11.11111112 Combine like terms: 11.11111111 + 11.11111112 = 22.22222223 11.11111112 + -6.666666667x + x2 = 22.22222223 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 22.22222223 Calculate the square root of the right side: 4.714045209 Break this problem into two subproblems by setting (x + -3.333333334) equal to 4.714045209 and -4.714045209.Subproblem 1
x + -3.333333334 = 4.714045209 Simplifying x + -3.333333334 = 4.714045209 Reorder the terms: -3.333333334 + x = 4.714045209 Solving -3.333333334 + x = 4.714045209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 4.714045209 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 4.714045209 + 3.333333334 x = 4.714045209 + 3.333333334 Combine like terms: 4.714045209 + 3.333333334 = 8.047378543 x = 8.047378543 Simplifying x = 8.047378543Subproblem 2
x + -3.333333334 = -4.714045209 Simplifying x + -3.333333334 = -4.714045209 Reorder the terms: -3.333333334 + x = -4.714045209 Solving -3.333333334 + x = -4.714045209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -4.714045209 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -4.714045209 + 3.333333334 x = -4.714045209 + 3.333333334 Combine like terms: -4.714045209 + 3.333333334 = -1.380711875 x = -1.380711875 Simplifying x = -1.380711875Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.047378543, -1.380711875}
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