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Simplifying 2x2 + 1x + -174 = 0 Reorder the terms: -174 + 1x + 2x2 = 0 Solving -174 + 1x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -87 + 0.5x + x2 = 0 Move the constant term to the right: Add '87' to each side of the equation. -87 + 0.5x + 87 + x2 = 0 + 87 Reorder the terms: -87 + 87 + 0.5x + x2 = 0 + 87 Combine like terms: -87 + 87 = 0 0 + 0.5x + x2 = 0 + 87 0.5x + x2 = 0 + 87 Combine like terms: 0 + 87 = 87 0.5x + x2 = 87 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 = 87 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 87 + 0.0625 Combine like terms: 87 + 0.0625 = 87.0625 0.0625 + 0.5x + x2 = 87.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 87.0625 Calculate the square root of the right side: 9.330728803 Break this problem into two subproblems by setting (x + 0.25) equal to 9.330728803 and -9.330728803.Subproblem 1
x + 0.25 = 9.330728803 Simplifying x + 0.25 = 9.330728803 Reorder the terms: 0.25 + x = 9.330728803 Solving 0.25 + x = 9.330728803 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 = 9.330728803 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 9.330728803 + -0.25 x = 9.330728803 + -0.25 Combine like terms: 9.330728803 + -0.25 = 9.080728803 x = 9.080728803 Simplifying x = 9.080728803Subproblem 2
x + 0.25 = -9.330728803 Simplifying x + 0.25 = -9.330728803 Reorder the terms: 0.25 + x = -9.330728803 Solving 0.25 + x = -9.330728803 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 = -9.330728803 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -9.330728803 + -0.25 x = -9.330728803 + -0.25 Combine like terms: -9.330728803 + -0.25 = -9.580728803 x = -9.580728803 Simplifying x = -9.580728803Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.080728803, -9.580728803}
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