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Simplifying 4x2 + -2x + -2.6 = 0 Reorder the terms: -2.6 + -2x + 4x2 = 0 Solving -2.6 + -2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.65 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.65' to each side of the equation. -0.65 + -0.5x + 0.65 + x2 = 0 + 0.65 Reorder the terms: -0.65 + 0.65 + -0.5x + x2 = 0 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + -0.5x + x2 = 0 + 0.65 -0.5x + x2 = 0 + 0.65 Combine like terms: 0 + 0.65 = 0.65 -0.5x + x2 = 0.65 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.65 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.65 + 0.0625 Combine like terms: 0.65 + 0.0625 = 0.7125 0.0625 + -0.5x + x2 = 0.7125 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.7125 Calculate the square root of the right side: 0.844097151 Break this problem into two subproblems by setting (x + -0.25) equal to 0.844097151 and -0.844097151.Subproblem 1
x + -0.25 = 0.844097151 Simplifying x + -0.25 = 0.844097151 Reorder the terms: -0.25 + x = 0.844097151 Solving -0.25 + x = 0.844097151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.844097151 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.844097151 + 0.25 x = 0.844097151 + 0.25 Combine like terms: 0.844097151 + 0.25 = 1.094097151 x = 1.094097151 Simplifying x = 1.094097151Subproblem 2
x + -0.25 = -0.844097151 Simplifying x + -0.25 = -0.844097151 Reorder the terms: -0.25 + x = -0.844097151 Solving -0.25 + x = -0.844097151 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.844097151 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.844097151 + 0.25 x = -0.844097151 + 0.25 Combine like terms: -0.844097151 + 0.25 = -0.594097151 x = -0.594097151 Simplifying x = -0.594097151Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.094097151, -0.594097151}
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