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Simplifying (5x2) + (-8x + 82) = 90 Reorder the terms: (5x2) + (82 + -8x) = 90 Remove parenthesis around (82 + -8x) (5x2) + 82 + -8x = 90 Reorder the terms: 82 + -8x + (5x2) = 90 Solving 82 + -8x + (5x2) = 90 Solving for variable 'x'. Reorder the terms: 82 + -90 + -8x + (5x2) = 90 + -90 Combine like terms: 82 + -90 = -8 -8 + -8x + (5x2) = 90 + -90 Combine like terms: 90 + -90 = 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 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 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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