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Simplifying -49x2 + 255x + 40 = 0 Reorder the terms: 40 + 255x + -49x2 = 0 Solving 40 + 255x + -49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -49 the coefficient of the squared term: Divide each side by '-49'. -0.8163265306 + -5.204081633x + x2 = 0 Move the constant term to the right: Add '0.8163265306' to each side of the equation. -0.8163265306 + -5.204081633x + 0.8163265306 + x2 = 0 + 0.8163265306 Reorder the terms: -0.8163265306 + 0.8163265306 + -5.204081633x + x2 = 0 + 0.8163265306 Combine like terms: -0.8163265306 + 0.8163265306 = 0.0000000000 0.0000000000 + -5.204081633x + x2 = 0 + 0.8163265306 -5.204081633x + x2 = 0 + 0.8163265306 Combine like terms: 0 + 0.8163265306 = 0.8163265306 -5.204081633x + x2 = 0.8163265306 The x term is -5.204081633x. Take half its coefficient (-2.602040817). Square it (6.770616413) and add it to both sides. Add '6.770616413' to each side of the equation. -5.204081633x + 6.770616413 + x2 = 0.8163265306 + 6.770616413 Reorder the terms: 6.770616413 + -5.204081633x + x2 = 0.8163265306 + 6.770616413 Combine like terms: 0.8163265306 + 6.770616413 = 7.5869429436 6.770616413 + -5.204081633x + x2 = 7.5869429436 Factor a perfect square on the left side: (x + -2.602040817)(x + -2.602040817) = 7.5869429436 Calculate the square root of the right side: 2.754440586 Break this problem into two subproblems by setting (x + -2.602040817) equal to 2.754440586 and -2.754440586.Subproblem 1
x + -2.602040817 = 2.754440586 Simplifying x + -2.602040817 = 2.754440586 Reorder the terms: -2.602040817 + x = 2.754440586 Solving -2.602040817 + x = 2.754440586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.602040817' to each side of the equation. -2.602040817 + 2.602040817 + x = 2.754440586 + 2.602040817 Combine like terms: -2.602040817 + 2.602040817 = 0.000000000 0.000000000 + x = 2.754440586 + 2.602040817 x = 2.754440586 + 2.602040817 Combine like terms: 2.754440586 + 2.602040817 = 5.356481403 x = 5.356481403 Simplifying x = 5.356481403Subproblem 2
x + -2.602040817 = -2.754440586 Simplifying x + -2.602040817 = -2.754440586 Reorder the terms: -2.602040817 + x = -2.754440586 Solving -2.602040817 + x = -2.754440586 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.602040817' to each side of the equation. -2.602040817 + 2.602040817 + x = -2.754440586 + 2.602040817 Combine like terms: -2.602040817 + 2.602040817 = 0.000000000 0.000000000 + x = -2.754440586 + 2.602040817 x = -2.754440586 + 2.602040817 Combine like terms: -2.754440586 + 2.602040817 = -0.152399769 x = -0.152399769 Simplifying x = -0.152399769Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.356481403, -0.152399769}
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