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Simplifying 0 = -4.9x2 + 13x + 500 Reorder the terms: 0 = 500 + 13x + -4.9x2 Solving 0 = 500 + 13x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -500 = -500 -500 + -13x + 4.9x2 = 500 + 13x + -4.9x2 + -500 + -13x + 4.9x2 Reorder the terms: -500 + -13x + 4.9x2 = 500 + -500 + 13x + -13x + -4.9x2 + 4.9x2 Combine like terms: 500 + -500 = 0 -500 + -13x + 4.9x2 = 0 + 13x + -13x + -4.9x2 + 4.9x2 -500 + -13x + 4.9x2 = 13x + -13x + -4.9x2 + 4.9x2 Combine like terms: 13x + -13x = 0 -500 + -13x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -500 + -13x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -500 + -13x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -102.0408163 + -2.653061224x + x2 = 0 Move the constant term to the right: Add '102.0408163' to each side of the equation. -102.0408163 + -2.653061224x + 102.0408163 + x2 = 0 + 102.0408163 Reorder the terms: -102.0408163 + 102.0408163 + -2.653061224x + x2 = 0 + 102.0408163 Combine like terms: -102.0408163 + 102.0408163 = 0.0000000 0.0000000 + -2.653061224x + x2 = 0 + 102.0408163 -2.653061224x + x2 = 0 + 102.0408163 Combine like terms: 0 + 102.0408163 = 102.0408163 -2.653061224x + x2 = 102.0408163 The x term is -2.653061224x. Take half its coefficient (-1.326530612). Square it (1.759683465) and add it to both sides. Add '1.759683465' to each side of the equation. -2.653061224x + 1.759683465 + x2 = 102.0408163 + 1.759683465 Reorder the terms: 1.759683465 + -2.653061224x + x2 = 102.0408163 + 1.759683465 Combine like terms: 102.0408163 + 1.759683465 = 103.800499765 1.759683465 + -2.653061224x + x2 = 103.800499765 Factor a perfect square on the left side: (x + -1.326530612)(x + -1.326530612) = 103.800499765 Calculate the square root of the right side: 10.188253028 Break this problem into two subproblems by setting (x + -1.326530612) equal to 10.188253028 and -10.188253028.Subproblem 1
x + -1.326530612 = 10.188253028 Simplifying x + -1.326530612 = 10.188253028 Reorder the terms: -1.326530612 + x = 10.188253028 Solving -1.326530612 + x = 10.188253028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + x = 10.188253028 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + x = 10.188253028 + 1.326530612 x = 10.188253028 + 1.326530612 Combine like terms: 10.188253028 + 1.326530612 = 11.51478364 x = 11.51478364 Simplifying x = 11.51478364Subproblem 2
x + -1.326530612 = -10.188253028 Simplifying x + -1.326530612 = -10.188253028 Reorder the terms: -1.326530612 + x = -10.188253028 Solving -1.326530612 + x = -10.188253028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.326530612' to each side of the equation. -1.326530612 + 1.326530612 + x = -10.188253028 + 1.326530612 Combine like terms: -1.326530612 + 1.326530612 = 0.000000000 0.000000000 + x = -10.188253028 + 1.326530612 x = -10.188253028 + 1.326530612 Combine like terms: -10.188253028 + 1.326530612 = -8.861722416 x = -8.861722416 Simplifying x = -8.861722416Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.51478364, -8.861722416}
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