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Simplifying 0 = -4.1x2 + 7.1x + 145 Reorder the terms: 0 = 145 + 7.1x + -4.1x2 Solving 0 = 145 + 7.1x + -4.1x2 Solving for variable 'x'. Combine like terms: 0 + -145 = -145 -145 + -7.1x + 4.1x2 = 145 + 7.1x + -4.1x2 + -145 + -7.1x + 4.1x2 Reorder the terms: -145 + -7.1x + 4.1x2 = 145 + -145 + 7.1x + -7.1x + -4.1x2 + 4.1x2 Combine like terms: 145 + -145 = 0 -145 + -7.1x + 4.1x2 = 0 + 7.1x + -7.1x + -4.1x2 + 4.1x2 -145 + -7.1x + 4.1x2 = 7.1x + -7.1x + -4.1x2 + 4.1x2 Combine like terms: 7.1x + -7.1x = 0.0 -145 + -7.1x + 4.1x2 = 0.0 + -4.1x2 + 4.1x2 -145 + -7.1x + 4.1x2 = -4.1x2 + 4.1x2 Combine like terms: -4.1x2 + 4.1x2 = 0.0 -145 + -7.1x + 4.1x2 = 0.0 Begin completing the square. Divide all terms by 4.1 the coefficient of the squared term: Divide each side by '4.1'. -35.36585366 + -1.731707317x + x2 = 0 Move the constant term to the right: Add '35.36585366' to each side of the equation. -35.36585366 + -1.731707317x + 35.36585366 + x2 = 0 + 35.36585366 Reorder the terms: -35.36585366 + 35.36585366 + -1.731707317x + x2 = 0 + 35.36585366 Combine like terms: -35.36585366 + 35.36585366 = 0.00000000 0.00000000 + -1.731707317x + x2 = 0 + 35.36585366 -1.731707317x + x2 = 0 + 35.36585366 Combine like terms: 0 + 35.36585366 = 35.36585366 -1.731707317x + x2 = 35.36585366 The x term is -1.731707317x. Take half its coefficient (-0.8658536585). Square it (0.7497025579) and add it to both sides. Add '0.7497025579' to each side of the equation. -1.731707317x + 0.7497025579 + x2 = 35.36585366 + 0.7497025579 Reorder the terms: 0.7497025579 + -1.731707317x + x2 = 35.36585366 + 0.7497025579 Combine like terms: 35.36585366 + 0.7497025579 = 36.1155562179 0.7497025579 + -1.731707317x + x2 = 36.1155562179 Factor a perfect square on the left side: (x + -0.8658536585)(x + -0.8658536585) = 36.1155562179 Calculate the square root of the right side: 6.00962197 Break this problem into two subproblems by setting (x + -0.8658536585) equal to 6.00962197 and -6.00962197.Subproblem 1
x + -0.8658536585 = 6.00962197 Simplifying x + -0.8658536585 = 6.00962197 Reorder the terms: -0.8658536585 + x = 6.00962197 Solving -0.8658536585 + x = 6.00962197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8658536585' to each side of the equation. -0.8658536585 + 0.8658536585 + x = 6.00962197 + 0.8658536585 Combine like terms: -0.8658536585 + 0.8658536585 = 0.0000000000 0.0000000000 + x = 6.00962197 + 0.8658536585 x = 6.00962197 + 0.8658536585 Combine like terms: 6.00962197 + 0.8658536585 = 6.8754756285 x = 6.8754756285 Simplifying x = 6.8754756285Subproblem 2
x + -0.8658536585 = -6.00962197 Simplifying x + -0.8658536585 = -6.00962197 Reorder the terms: -0.8658536585 + x = -6.00962197 Solving -0.8658536585 + x = -6.00962197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8658536585' to each side of the equation. -0.8658536585 + 0.8658536585 + x = -6.00962197 + 0.8658536585 Combine like terms: -0.8658536585 + 0.8658536585 = 0.0000000000 0.0000000000 + x = -6.00962197 + 0.8658536585 x = -6.00962197 + 0.8658536585 Combine like terms: -6.00962197 + 0.8658536585 = -5.1437683115 x = -5.1437683115 Simplifying x = -5.1437683115Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.8754756285, -5.1437683115}
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