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Simplifying 5x2 + 10x + -64 = 0 Reorder the terms: -64 + 10x + 5x2 = 0 Solving -64 + 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'. -12.8 + 2x + x2 = 0 Move the constant term to the right: Add '12.8' to each side of the equation. -12.8 + 2x + 12.8 + x2 = 0 + 12.8 Reorder the terms: -12.8 + 12.8 + 2x + x2 = 0 + 12.8 Combine like terms: -12.8 + 12.8 = 0.0 0.0 + 2x + x2 = 0 + 12.8 2x + x2 = 0 + 12.8 Combine like terms: 0 + 12.8 = 12.8 2x + x2 = 12.8 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 = 12.8 + 1 Reorder the terms: 1 + 2x + x2 = 12.8 + 1 Combine like terms: 12.8 + 1 = 13.8 1 + 2x + x2 = 13.8 Factor a perfect square on the left side: (x + 1)(x + 1) = 13.8 Calculate the square root of the right side: 3.714835124 Break this problem into two subproblems by setting (x + 1) equal to 3.714835124 and -3.714835124.Subproblem 1
x + 1 = 3.714835124 Simplifying x + 1 = 3.714835124 Reorder the terms: 1 + x = 3.714835124 Solving 1 + x = 3.714835124 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 = 3.714835124 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.714835124 + -1 x = 3.714835124 + -1 Combine like terms: 3.714835124 + -1 = 2.714835124 x = 2.714835124 Simplifying x = 2.714835124Subproblem 2
x + 1 = -3.714835124 Simplifying x + 1 = -3.714835124 Reorder the terms: 1 + x = -3.714835124 Solving 1 + x = -3.714835124 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 = -3.714835124 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.714835124 + -1 x = -3.714835124 + -1 Combine like terms: -3.714835124 + -1 = -4.714835124 x = -4.714835124 Simplifying x = -4.714835124Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.714835124, -4.714835124}
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