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Simplifying 400 = 15x2 + 64x + 360 Reorder the terms: 400 = 360 + 64x + 15x2 Solving 400 = 360 + 64x + 15x2 Solving for variable 'x'. Combine like terms: 400 + -360 = 40 40 + -64x + -15x2 = 360 + 64x + 15x2 + -360 + -64x + -15x2 Reorder the terms: 40 + -64x + -15x2 = 360 + -360 + 64x + -64x + 15x2 + -15x2 Combine like terms: 360 + -360 = 0 40 + -64x + -15x2 = 0 + 64x + -64x + 15x2 + -15x2 40 + -64x + -15x2 = 64x + -64x + 15x2 + -15x2 Combine like terms: 64x + -64x = 0 40 + -64x + -15x2 = 0 + 15x2 + -15x2 40 + -64x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 40 + -64x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -2.666666667 + 4.266666667x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 4.266666667x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 4.266666667x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 4.266666667x + x2 = 0 + 2.666666667 4.266666667x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 4.266666667x + x2 = 2.666666667 The x term is 4.266666667x. Take half its coefficient (2.133333334). Square it (4.551111114) and add it to both sides. Add '4.551111114' to each side of the equation. 4.266666667x + 4.551111114 + x2 = 2.666666667 + 4.551111114 Reorder the terms: 4.551111114 + 4.266666667x + x2 = 2.666666667 + 4.551111114 Combine like terms: 2.666666667 + 4.551111114 = 7.217777781 4.551111114 + 4.266666667x + x2 = 7.217777781 Factor a perfect square on the left side: (x + 2.133333334)(x + 2.133333334) = 7.217777781 Calculate the square root of the right side: 2.686592225 Break this problem into two subproblems by setting (x + 2.133333334) equal to 2.686592225 and -2.686592225.Subproblem 1
x + 2.133333334 = 2.686592225 Simplifying x + 2.133333334 = 2.686592225 Reorder the terms: 2.133333334 + x = 2.686592225 Solving 2.133333334 + x = 2.686592225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.133333334' to each side of the equation. 2.133333334 + -2.133333334 + x = 2.686592225 + -2.133333334 Combine like terms: 2.133333334 + -2.133333334 = 0.000000000 0.000000000 + x = 2.686592225 + -2.133333334 x = 2.686592225 + -2.133333334 Combine like terms: 2.686592225 + -2.133333334 = 0.553258891 x = 0.553258891 Simplifying x = 0.553258891Subproblem 2
x + 2.133333334 = -2.686592225 Simplifying x + 2.133333334 = -2.686592225 Reorder the terms: 2.133333334 + x = -2.686592225 Solving 2.133333334 + x = -2.686592225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.133333334' to each side of the equation. 2.133333334 + -2.133333334 + x = -2.686592225 + -2.133333334 Combine like terms: 2.133333334 + -2.133333334 = 0.000000000 0.000000000 + x = -2.686592225 + -2.133333334 x = -2.686592225 + -2.133333334 Combine like terms: -2.686592225 + -2.133333334 = -4.819925559 x = -4.819925559 Simplifying x = -4.819925559Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.553258891, -4.819925559}
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