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Simplifying 18x2 + 25x + -15 = 0 Reorder the terms: -15 + 25x + 18x2 = 0 Solving -15 + 25x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.8333333333 + 1.388888889x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 1.388888889x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 1.388888889x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 1.388888889x + x2 = 0 + 0.8333333333 1.388888889x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 1.388888889x + x2 = 0.8333333333 The x term is 1.388888889x. Take half its coefficient (0.6944444445). Square it (0.4822530865) and add it to both sides. Add '0.4822530865' to each side of the equation. 1.388888889x + 0.4822530865 + x2 = 0.8333333333 + 0.4822530865 Reorder the terms: 0.4822530865 + 1.388888889x + x2 = 0.8333333333 + 0.4822530865 Combine like terms: 0.8333333333 + 0.4822530865 = 1.3155864198 0.4822530865 + 1.388888889x + x2 = 1.3155864198 Factor a perfect square on the left side: (x + 0.6944444445)(x + 0.6944444445) = 1.3155864198 Calculate the square root of the right side: 1.146990157 Break this problem into two subproblems by setting (x + 0.6944444445) equal to 1.146990157 and -1.146990157.Subproblem 1
x + 0.6944444445 = 1.146990157 Simplifying x + 0.6944444445 = 1.146990157 Reorder the terms: 0.6944444445 + x = 1.146990157 Solving 0.6944444445 + x = 1.146990157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6944444445' to each side of the equation. 0.6944444445 + -0.6944444445 + x = 1.146990157 + -0.6944444445 Combine like terms: 0.6944444445 + -0.6944444445 = 0.0000000000 0.0000000000 + x = 1.146990157 + -0.6944444445 x = 1.146990157 + -0.6944444445 Combine like terms: 1.146990157 + -0.6944444445 = 0.4525457125 x = 0.4525457125 Simplifying x = 0.4525457125Subproblem 2
x + 0.6944444445 = -1.146990157 Simplifying x + 0.6944444445 = -1.146990157 Reorder the terms: 0.6944444445 + x = -1.146990157 Solving 0.6944444445 + x = -1.146990157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6944444445' to each side of the equation. 0.6944444445 + -0.6944444445 + x = -1.146990157 + -0.6944444445 Combine like terms: 0.6944444445 + -0.6944444445 = 0.0000000000 0.0000000000 + x = -1.146990157 + -0.6944444445 x = -1.146990157 + -0.6944444445 Combine like terms: -1.146990157 + -0.6944444445 = -1.8414346015 x = -1.8414346015 Simplifying x = -1.8414346015Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4525457125, -1.8414346015}
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