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Simplifying 5x2 + 10x + -8 = 0 Reorder the terms: -8 + 10x + 5x2 = 0 Solving -8 + 10x + 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'. -1.6 + 2x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 2x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 2x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 2x + x2 = 0 + 1.6 2x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 2x + x2 = 1.6 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.6 + 1 Reorder the terms: 1 + 2x + x2 = 1.6 + 1 Combine like terms: 1.6 + 1 = 2.6 1 + 2x + x2 = 2.6 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.6 Calculate the square root of the right side: 1.61245155 Break this problem into two subproblems by setting (x + 1) equal to 1.61245155 and -1.61245155.Subproblem 1
x + 1 = 1.61245155 Simplifying x + 1 = 1.61245155 Reorder the terms: 1 + x = 1.61245155 Solving 1 + x = 1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.61245155 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.61245155 + -1 x = 1.61245155 + -1 Combine like terms: 1.61245155 + -1 = 0.61245155 x = 0.61245155 Simplifying x = 0.61245155Subproblem 2
x + 1 = -1.61245155 Simplifying x + 1 = -1.61245155 Reorder the terms: 1 + x = -1.61245155 Solving 1 + x = -1.61245155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.61245155 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.61245155 + -1 x = -1.61245155 + -1 Combine like terms: -1.61245155 + -1 = -2.61245155 x = -2.61245155 Simplifying x = -2.61245155Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.61245155, -2.61245155}
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