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Simplifying -1.716x2 + 1.716x + 10 = 0 Reorder the terms: 10 + 1.716x + -1.716x2 = 0 Solving 10 + 1.716x + -1.716x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.716 the coefficient of the squared term: Divide each side by '-1.716'. -5.827505828 + -1x + x2 = 0 Move the constant term to the right: Add '5.827505828' to each side of the equation. -5.827505828 + -1x + 5.827505828 + x2 = 0 + 5.827505828 Reorder the terms: -5.827505828 + 5.827505828 + -1x + x2 = 0 + 5.827505828 Combine like terms: -5.827505828 + 5.827505828 = 0.000000000 0.000000000 + -1x + x2 = 0 + 5.827505828 -1x + x2 = 0 + 5.827505828 Combine like terms: 0 + 5.827505828 = 5.827505828 -1x + x2 = 5.827505828 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 5.827505828 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5.827505828 + 0.25 Combine like terms: 5.827505828 + 0.25 = 6.077505828 0.25 + -1x + x2 = 6.077505828 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.077505828 Calculate the square root of the right side: 2.465259789 Break this problem into two subproblems by setting (x + -0.5) equal to 2.465259789 and -2.465259789.Subproblem 1
x + -0.5 = 2.465259789 Simplifying x + -0.5 = 2.465259789 Reorder the terms: -0.5 + x = 2.465259789 Solving -0.5 + x = 2.465259789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.465259789 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.465259789 + 0.5 x = 2.465259789 + 0.5 Combine like terms: 2.465259789 + 0.5 = 2.965259789 x = 2.965259789 Simplifying x = 2.965259789Subproblem 2
x + -0.5 = -2.465259789 Simplifying x + -0.5 = -2.465259789 Reorder the terms: -0.5 + x = -2.465259789 Solving -0.5 + x = -2.465259789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.465259789 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.465259789 + 0.5 x = -2.465259789 + 0.5 Combine like terms: -2.465259789 + 0.5 = -1.965259789 x = -1.965259789 Simplifying x = -1.965259789Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.965259789, -1.965259789}
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