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Simplifying -1x2 + -40x + -9 = 0 Reorder the terms: -9 + -40x + -1x2 = 0 Solving -9 + -40x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 40x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 40x + x2)' equal to zero and attempt to solve: Simplifying 9 + 40x + x2 = 0 Solving 9 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 40x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 40x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 40x + x2 = 0 + -9 40x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 40x + x2 = -9 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -9 + 400 Reorder the terms: 400 + 40x + x2 = -9 + 400 Combine like terms: -9 + 400 = 391 400 + 40x + x2 = 391 Factor a perfect square on the left side: (x + 20)(x + 20) = 391 Calculate the square root of the right side: 19.773719933 Break this problem into two subproblems by setting (x + 20) equal to 19.773719933 and -19.773719933.Subproblem 1
x + 20 = 19.773719933 Simplifying x + 20 = 19.773719933 Reorder the terms: 20 + x = 19.773719933 Solving 20 + x = 19.773719933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 19.773719933 + -20 Combine like terms: 20 + -20 = 0 0 + x = 19.773719933 + -20 x = 19.773719933 + -20 Combine like terms: 19.773719933 + -20 = -0.226280067 x = -0.226280067 Simplifying x = -0.226280067Subproblem 2
x + 20 = -19.773719933 Simplifying x + 20 = -19.773719933 Reorder the terms: 20 + x = -19.773719933 Solving 20 + x = -19.773719933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -19.773719933 + -20 Combine like terms: 20 + -20 = 0 0 + x = -19.773719933 + -20 x = -19.773719933 + -20 Combine like terms: -19.773719933 + -20 = -39.773719933 x = -39.773719933 Simplifying x = -39.773719933Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.226280067, -39.773719933}Solution
x = {-0.226280067, -39.773719933}
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