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Simplifying -5x2 + 9x + 8 = x Reorder the terms: 8 + 9x + -5x2 = x Solving 8 + 9x + -5x2 = x Solving for variable 'x'. Reorder the terms: 8 + 9x + -1x + -5x2 = x + -1x Combine like terms: 9x + -1x = 8x 8 + 8x + -5x2 = x + -1x Combine like terms: x + -1x = 0 8 + 8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.6 + -1.6x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.6x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.6x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.6x + x2 = 0 + 1.6 -1.6x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.6x + x2 = 1.6 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 = 1.6 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 1.6 + 0.64 Combine like terms: 1.6 + 0.64 = 2.24 0.64 + -1.6x + x2 = 2.24 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (x + -0.8) equal to 1.496662955 and -1.496662955.Subproblem 1
x + -0.8 = 1.496662955 Simplifying x + -0.8 = 1.496662955 Reorder the terms: -0.8 + x = 1.496662955 Solving -0.8 + x = 1.496662955 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 = 1.496662955 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 1.496662955 + 0.8 x = 1.496662955 + 0.8 Combine like terms: 1.496662955 + 0.8 = 2.296662955 x = 2.296662955 Simplifying x = 2.296662955Subproblem 2
x + -0.8 = -1.496662955 Simplifying x + -0.8 = -1.496662955 Reorder the terms: -0.8 + x = -1.496662955 Solving -0.8 + x = -1.496662955 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 = -1.496662955 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -1.496662955 + 0.8 x = -1.496662955 + 0.8 Combine like terms: -1.496662955 + 0.8 = -0.696662955 x = -0.696662955 Simplifying x = -0.696662955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.296662955, -0.696662955}
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