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Simplifying -37x2 + 21x = -178 Reorder the terms: 21x + -37x2 = -178 Solving 21x + -37x2 = -178 Solving for variable 'x'. Reorder the terms: 178 + 21x + -37x2 = -178 + 178 Combine like terms: -178 + 178 = 0 178 + 21x + -37x2 = 0 Begin completing the square. Divide all terms by -37 the coefficient of the squared term: Divide each side by '-37'. -4.810810811 + -0.5675675676x + x2 = 0 Move the constant term to the right: Add '4.810810811' to each side of the equation. -4.810810811 + -0.5675675676x + 4.810810811 + x2 = 0 + 4.810810811 Reorder the terms: -4.810810811 + 4.810810811 + -0.5675675676x + x2 = 0 + 4.810810811 Combine like terms: -4.810810811 + 4.810810811 = 0.000000000 0.000000000 + -0.5675675676x + x2 = 0 + 4.810810811 -0.5675675676x + x2 = 0 + 4.810810811 Combine like terms: 0 + 4.810810811 = 4.810810811 -0.5675675676x + x2 = 4.810810811 The x term is -0.5675675676x. Take half its coefficient (-0.2837837838). Square it (0.08053323595) and add it to both sides. Add '0.08053323595' to each side of the equation. -0.5675675676x + 0.08053323595 + x2 = 4.810810811 + 0.08053323595 Reorder the terms: 0.08053323595 + -0.5675675676x + x2 = 4.810810811 + 0.08053323595 Combine like terms: 4.810810811 + 0.08053323595 = 4.89134404695 0.08053323595 + -0.5675675676x + x2 = 4.89134404695 Factor a perfect square on the left side: (x + -0.2837837838)(x + -0.2837837838) = 4.89134404695 Calculate the square root of the right side: 2.211638317 Break this problem into two subproblems by setting (x + -0.2837837838) equal to 2.211638317 and -2.211638317.Subproblem 1
x + -0.2837837838 = 2.211638317 Simplifying x + -0.2837837838 = 2.211638317 Reorder the terms: -0.2837837838 + x = 2.211638317 Solving -0.2837837838 + x = 2.211638317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2837837838' to each side of the equation. -0.2837837838 + 0.2837837838 + x = 2.211638317 + 0.2837837838 Combine like terms: -0.2837837838 + 0.2837837838 = 0.0000000000 0.0000000000 + x = 2.211638317 + 0.2837837838 x = 2.211638317 + 0.2837837838 Combine like terms: 2.211638317 + 0.2837837838 = 2.4954221008 x = 2.4954221008 Simplifying x = 2.4954221008Subproblem 2
x + -0.2837837838 = -2.211638317 Simplifying x + -0.2837837838 = -2.211638317 Reorder the terms: -0.2837837838 + x = -2.211638317 Solving -0.2837837838 + x = -2.211638317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2837837838' to each side of the equation. -0.2837837838 + 0.2837837838 + x = -2.211638317 + 0.2837837838 Combine like terms: -0.2837837838 + 0.2837837838 = 0.0000000000 0.0000000000 + x = -2.211638317 + 0.2837837838 x = -2.211638317 + 0.2837837838 Combine like terms: -2.211638317 + 0.2837837838 = -1.9278545332 x = -1.9278545332 Simplifying x = -1.9278545332Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4954221008, -1.9278545332}
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