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Simplifying 5x2 + -8x + -90 = 0 Reorder the terms: -90 + -8x + 5x2 = 0 Solving -90 + -8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18 + -1.6x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -1.6x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -1.6x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1.6x + x2 = 0 + 18 -1.6x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -1.6x + x2 = 18 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 18 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 18 + 0.64 Combine like terms: 18 + 0.64 = 18.64 0.64 + -1.6x + x2 = 18.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 18.64 Calculate the square root of the right side: 4.317406629 Break this problem into two subproblems by setting (x + -0.8) equal to 4.317406629 and -4.317406629.Subproblem 1
x + -0.8 = 4.317406629 Simplifying x + -0.8 = 4.317406629 Reorder the terms: -0.8 + x = 4.317406629 Solving -0.8 + x = 4.317406629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 4.317406629 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 4.317406629 + 0.8 x = 4.317406629 + 0.8 Combine like terms: 4.317406629 + 0.8 = 5.117406629 x = 5.117406629 Simplifying x = 5.117406629Subproblem 2
x + -0.8 = -4.317406629 Simplifying x + -0.8 = -4.317406629 Reorder the terms: -0.8 + x = -4.317406629 Solving -0.8 + x = -4.317406629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -4.317406629 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -4.317406629 + 0.8 x = -4.317406629 + 0.8 Combine like terms: -4.317406629 + 0.8 = -3.517406629 x = -3.517406629 Simplifying x = -3.517406629Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.117406629, -3.517406629}
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