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Simplifying 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 = 1.380711875 x = 1.380711875 Simplifying x = 1.380711875Subproblem 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 = -8.047378543 x = -8.047378543 Simplifying x = -8.047378543Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.380711875, -8.047378543}
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