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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 = 1.884444447 4.551111114 + -4.266666667x + x2 = 1.884444447 Factor a perfect square on the left side: (x + -2.133333334)(x + -2.133333334) = 1.884444447 Calculate the square root of the right side: 1.372750686 Break this problem into two subproblems by setting (x + -2.133333334) equal to 1.372750686 and -1.372750686.Subproblem 1
x + -2.133333334 = 1.372750686 Simplifying x + -2.133333334 = 1.372750686 Reorder the terms: -2.133333334 + x = 1.372750686 Solving -2.133333334 + x = 1.372750686 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 = 1.372750686 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = 1.372750686 + 2.133333334 x = 1.372750686 + 2.133333334 Combine like terms: 1.372750686 + 2.133333334 = 3.50608402 x = 3.50608402 Simplifying x = 3.50608402Subproblem 2
x + -2.133333334 = -1.372750686 Simplifying x + -2.133333334 = -1.372750686 Reorder the terms: -2.133333334 + x = -1.372750686 Solving -2.133333334 + x = -1.372750686 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 = -1.372750686 + 2.133333334 Combine like terms: -2.133333334 + 2.133333334 = 0.000000000 0.000000000 + x = -1.372750686 + 2.133333334 x = -1.372750686 + 2.133333334 Combine like terms: -1.372750686 + 2.133333334 = 0.760582648 x = 0.760582648 Simplifying x = 0.760582648Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.50608402, 0.760582648}
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