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Simplifying 4x2 + -29x + -90 = 0 Reorder the terms: -90 + -29x + 4x2 = 0 Solving -90 + -29x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -22.5 + -7.25x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -7.25x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -7.25x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -7.25x + x2 = 0 + 22.5 -7.25x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -7.25x + x2 = 22.5 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = 22.5 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 22.5 + 13.140625 Combine like terms: 22.5 + 13.140625 = 35.640625 13.140625 + -7.25x + x2 = 35.640625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 35.640625 Calculate the square root of the right side: 5.969976968 Break this problem into two subproblems by setting (x + -3.625) equal to 5.969976968 and -5.969976968.Subproblem 1
x + -3.625 = 5.969976968 Simplifying x + -3.625 = 5.969976968 Reorder the terms: -3.625 + x = 5.969976968 Solving -3.625 + x = 5.969976968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 5.969976968 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 5.969976968 + 3.625 x = 5.969976968 + 3.625 Combine like terms: 5.969976968 + 3.625 = 9.594976968 x = 9.594976968 Simplifying x = 9.594976968Subproblem 2
x + -3.625 = -5.969976968 Simplifying x + -3.625 = -5.969976968 Reorder the terms: -3.625 + x = -5.969976968 Solving -3.625 + x = -5.969976968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -5.969976968 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -5.969976968 + 3.625 x = -5.969976968 + 3.625 Combine like terms: -5.969976968 + 3.625 = -2.344976968 x = -2.344976968 Simplifying x = -2.344976968Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.594976968, -2.344976968}
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