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Simplifying 167x2 = 7.58x + 29.28 Reorder the terms: 167x2 = 29.28 + 7.58x Solving 167x2 = 29.28 + 7.58x Solving for variable 'x'. Reorder the terms: -29.28 + -7.58x + 167x2 = 29.28 + 7.58x + -29.28 + -7.58x Reorder the terms: -29.28 + -7.58x + 167x2 = 29.28 + -29.28 + 7.58x + -7.58x Combine like terms: 29.28 + -29.28 = 0.00 -29.28 + -7.58x + 167x2 = 0.00 + 7.58x + -7.58x -29.28 + -7.58x + 167x2 = 7.58x + -7.58x Combine like terms: 7.58x + -7.58x = 0.00 -29.28 + -7.58x + 167x2 = 0.00 Begin completing the square. Divide all terms by 167 the coefficient of the squared term: Divide each side by '167'. -0.1753293413 + -0.04538922156x + x2 = 0.00 Move the constant term to the right: Add '0.1753293413' to each side of the equation. -0.1753293413 + -0.04538922156x + 0.1753293413 + x2 = 0.00 + 0.1753293413 Reorder the terms: -0.1753293413 + 0.1753293413 + -0.04538922156x + x2 = 0.00 + 0.1753293413 Combine like terms: -0.1753293413 + 0.1753293413 = 0.0000000000 0.0000000000 + -0.04538922156x + x2 = 0.00 + 0.1753293413 -0.04538922156x + x2 = 0.00 + 0.1753293413 Combine like terms: 0.00 + 0.1753293413 = 0.1753293413 -0.04538922156x + x2 = 0.1753293413 The x term is -0.04538922156x. Take half its coefficient (-0.02269461078). Square it (0.0005150453585) and add it to both sides. Add '0.0005150453585' to each side of the equation. -0.04538922156x + 0.0005150453585 + x2 = 0.1753293413 + 0.0005150453585 Reorder the terms: 0.0005150453585 + -0.04538922156x + x2 = 0.1753293413 + 0.0005150453585 Combine like terms: 0.1753293413 + 0.0005150453585 = 0.1758443866585 0.0005150453585 + -0.04538922156x + x2 = 0.1758443866585 Factor a perfect square on the left side: (x + -0.02269461078)(x + -0.02269461078) = 0.1758443866585 Calculate the square root of the right side: 0.419338034 Break this problem into two subproblems by setting (x + -0.02269461078) equal to 0.419338034 and -0.419338034.Subproblem 1
x + -0.02269461078 = 0.419338034 Simplifying x + -0.02269461078 = 0.419338034 Reorder the terms: -0.02269461078 + x = 0.419338034 Solving -0.02269461078 + x = 0.419338034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02269461078' to each side of the equation. -0.02269461078 + 0.02269461078 + x = 0.419338034 + 0.02269461078 Combine like terms: -0.02269461078 + 0.02269461078 = 0.00000000000 0.00000000000 + x = 0.419338034 + 0.02269461078 x = 0.419338034 + 0.02269461078 Combine like terms: 0.419338034 + 0.02269461078 = 0.44203264478 x = 0.44203264478 Simplifying x = 0.44203264478Subproblem 2
x + -0.02269461078 = -0.419338034 Simplifying x + -0.02269461078 = -0.419338034 Reorder the terms: -0.02269461078 + x = -0.419338034 Solving -0.02269461078 + x = -0.419338034 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02269461078' to each side of the equation. -0.02269461078 + 0.02269461078 + x = -0.419338034 + 0.02269461078 Combine like terms: -0.02269461078 + 0.02269461078 = 0.00000000000 0.00000000000 + x = -0.419338034 + 0.02269461078 x = -0.419338034 + 0.02269461078 Combine like terms: -0.419338034 + 0.02269461078 = -0.39664342322 x = -0.39664342322 Simplifying x = -0.39664342322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.44203264478, -0.39664342322}
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