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Simplifying 5x2 + -62x + -40 = 0 Reorder the terms: -40 + -62x + 5x2 = 0 Solving -40 + -62x + 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'. -8 + -12.4x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -12.4x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -12.4x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -12.4x + x2 = 0 + 8 -12.4x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -12.4x + x2 = 8 The x term is -12.4x. Take half its coefficient (-6.2). Square it (38.44) and add it to both sides. Add '38.44' to each side of the equation. -12.4x + 38.44 + x2 = 8 + 38.44 Reorder the terms: 38.44 + -12.4x + x2 = 8 + 38.44 Combine like terms: 8 + 38.44 = 46.44 38.44 + -12.4x + x2 = 46.44 Factor a perfect square on the left side: (x + -6.2)(x + -6.2) = 46.44 Calculate the square root of the right side: 6.814690015 Break this problem into two subproblems by setting (x + -6.2) equal to 6.814690015 and -6.814690015.Subproblem 1
x + -6.2 = 6.814690015 Simplifying x + -6.2 = 6.814690015 Reorder the terms: -6.2 + x = 6.814690015 Solving -6.2 + x = 6.814690015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + x = 6.814690015 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + x = 6.814690015 + 6.2 x = 6.814690015 + 6.2 Combine like terms: 6.814690015 + 6.2 = 13.014690015 x = 13.014690015 Simplifying x = 13.014690015Subproblem 2
x + -6.2 = -6.814690015 Simplifying x + -6.2 = -6.814690015 Reorder the terms: -6.2 + x = -6.814690015 Solving -6.2 + x = -6.814690015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.2' to each side of the equation. -6.2 + 6.2 + x = -6.814690015 + 6.2 Combine like terms: -6.2 + 6.2 = 0.0 0.0 + x = -6.814690015 + 6.2 x = -6.814690015 + 6.2 Combine like terms: -6.814690015 + 6.2 = -0.614690015 x = -0.614690015 Simplifying x = -0.614690015Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.014690015, -0.614690015}
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