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Simplifying 4x2 + -26x + -56.25 = 0 Reorder the terms: -56.25 + -26x + 4x2 = 0 Solving -56.25 + -26x + 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'. -14.0625 + -6.5x + x2 = 0 Move the constant term to the right: Add '14.0625' to each side of the equation. -14.0625 + -6.5x + 14.0625 + x2 = 0 + 14.0625 Reorder the terms: -14.0625 + 14.0625 + -6.5x + x2 = 0 + 14.0625 Combine like terms: -14.0625 + 14.0625 = 0.0000 0.0000 + -6.5x + x2 = 0 + 14.0625 -6.5x + x2 = 0 + 14.0625 Combine like terms: 0 + 14.0625 = 14.0625 -6.5x + x2 = 14.0625 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 14.0625 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 14.0625 + 10.5625 Combine like terms: 14.0625 + 10.5625 = 24.625 10.5625 + -6.5x + x2 = 24.625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 24.625 Calculate the square root of the right side: 4.96235831 Break this problem into two subproblems by setting (x + -3.25) equal to 4.96235831 and -4.96235831.Subproblem 1
x + -3.25 = 4.96235831 Simplifying x + -3.25 = 4.96235831 Reorder the terms: -3.25 + x = 4.96235831 Solving -3.25 + x = 4.96235831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.96235831 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.96235831 + 3.25 x = 4.96235831 + 3.25 Combine like terms: 4.96235831 + 3.25 = 8.21235831 x = 8.21235831 Simplifying x = 8.21235831Subproblem 2
x + -3.25 = -4.96235831 Simplifying x + -3.25 = -4.96235831 Reorder the terms: -3.25 + x = -4.96235831 Solving -3.25 + x = -4.96235831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.96235831 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.96235831 + 3.25 x = -4.96235831 + 3.25 Combine like terms: -4.96235831 + 3.25 = -1.71235831 x = -1.71235831 Simplifying x = -1.71235831Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.21235831, -1.71235831}
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