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Simplifying x2 + -41x + -90 = 0 Reorder the terms: -90 + -41x + x2 = 0 Solving -90 + -41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -41x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -41x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -41x + x2 = 0 + 90 -41x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -41x + x2 = 90 The x term is -41x. Take half its coefficient (-20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. -41x + 420.25 + x2 = 90 + 420.25 Reorder the terms: 420.25 + -41x + x2 = 90 + 420.25 Combine like terms: 90 + 420.25 = 510.25 420.25 + -41x + x2 = 510.25 Factor a perfect square on the left side: (x + -20.5)(x + -20.5) = 510.25 Calculate the square root of the right side: 22.588713996 Break this problem into two subproblems by setting (x + -20.5) equal to 22.588713996 and -22.588713996.Subproblem 1
x + -20.5 = 22.588713996 Simplifying x + -20.5 = 22.588713996 Reorder the terms: -20.5 + x = 22.588713996 Solving -20.5 + x = 22.588713996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = 22.588713996 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = 22.588713996 + 20.5 x = 22.588713996 + 20.5 Combine like terms: 22.588713996 + 20.5 = 43.088713996 x = 43.088713996 Simplifying x = 43.088713996Subproblem 2
x + -20.5 = -22.588713996 Simplifying x + -20.5 = -22.588713996 Reorder the terms: -20.5 + x = -22.588713996 Solving -20.5 + x = -22.588713996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.5' to each side of the equation. -20.5 + 20.5 + x = -22.588713996 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + x = -22.588713996 + 20.5 x = -22.588713996 + 20.5 Combine like terms: -22.588713996 + 20.5 = -2.088713996 x = -2.088713996 Simplifying x = -2.088713996Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.088713996, -2.088713996}
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