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Simplifying (32x + -0.03x2) + -1(5x + 13) = 0 Remove parenthesis around (32x + -0.03x2) 32x + -0.03x2 + -1(5x + 13) = 0 Reorder the terms: 32x + -0.03x2 + -1(13 + 5x) = 0 32x + -0.03x2 + (13 * -1 + 5x * -1) = 0 32x + -0.03x2 + (-13 + -5x) = 0 Reorder the terms: -13 + 32x + -5x + -0.03x2 = 0 Combine like terms: 32x + -5x = 27x -13 + 27x + -0.03x2 = 0 Solving -13 + 27x + -0.03x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. 433.3333333 + -900x + x2 = 0 Move the constant term to the right: Add '-433.3333333' to each side of the equation. 433.3333333 + -900x + -433.3333333 + x2 = 0 + -433.3333333 Reorder the terms: 433.3333333 + -433.3333333 + -900x + x2 = 0 + -433.3333333 Combine like terms: 433.3333333 + -433.3333333 = 0.0000000 0.0000000 + -900x + x2 = 0 + -433.3333333 -900x + x2 = 0 + -433.3333333 Combine like terms: 0 + -433.3333333 = -433.3333333 -900x + x2 = -433.3333333 The x term is -900x. Take half its coefficient (-450). Square it (202500) and add it to both sides. Add '202500' to each side of the equation. -900x + 202500 + x2 = -433.3333333 + 202500 Reorder the terms: 202500 + -900x + x2 = -433.3333333 + 202500 Combine like terms: -433.3333333 + 202500 = 202066.6666667 202500 + -900x + x2 = 202066.6666667 Factor a perfect square on the left side: (x + -450)(x + -450) = 202066.6666667 Calculate the square root of the right side: 449.51826066 Break this problem into two subproblems by setting (x + -450) equal to 449.51826066 and -449.51826066.Subproblem 1
x + -450 = 449.51826066 Simplifying x + -450 = 449.51826066 Reorder the terms: -450 + x = 449.51826066 Solving -450 + x = 449.51826066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = 449.51826066 + 450 Combine like terms: -450 + 450 = 0 0 + x = 449.51826066 + 450 x = 449.51826066 + 450 Combine like terms: 449.51826066 + 450 = 899.51826066 x = 899.51826066 Simplifying x = 899.51826066Subproblem 2
x + -450 = -449.51826066 Simplifying x + -450 = -449.51826066 Reorder the terms: -450 + x = -449.51826066 Solving -450 + x = -449.51826066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '450' to each side of the equation. -450 + 450 + x = -449.51826066 + 450 Combine like terms: -450 + 450 = 0 0 + x = -449.51826066 + 450 x = -449.51826066 + 450 Combine like terms: -449.51826066 + 450 = 0.48173934 x = 0.48173934 Simplifying x = 0.48173934Solution
The solution to the problem is based on the solutions from the subproblems. x = {899.51826066, 0.48173934}
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