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Simplifying 40x2 + 67x + -28 = 0 Reorder the terms: -28 + 67x + 40x2 = 0 Solving -28 + 67x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.7 + 1.675x + x2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + 1.675x + 0.7 + x2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + 1.675x + x2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + 1.675x + x2 = 0 + 0.7 1.675x + x2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 1.675x + x2 = 0.7 The x term is 1.675x. Take half its coefficient (0.8375). Square it (0.70140625) and add it to both sides. Add '0.70140625' to each side of the equation. 1.675x + 0.70140625 + x2 = 0.7 + 0.70140625 Reorder the terms: 0.70140625 + 1.675x + x2 = 0.7 + 0.70140625 Combine like terms: 0.7 + 0.70140625 = 1.40140625 0.70140625 + 1.675x + x2 = 1.40140625 Factor a perfect square on the left side: (x + 0.8375)(x + 0.8375) = 1.40140625 Calculate the square root of the right side: 1.183810057 Break this problem into two subproblems by setting (x + 0.8375) equal to 1.183810057 and -1.183810057.Subproblem 1
x + 0.8375 = 1.183810057 Simplifying x + 0.8375 = 1.183810057 Reorder the terms: 0.8375 + x = 1.183810057 Solving 0.8375 + x = 1.183810057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8375' to each side of the equation. 0.8375 + -0.8375 + x = 1.183810057 + -0.8375 Combine like terms: 0.8375 + -0.8375 = 0.0000 0.0000 + x = 1.183810057 + -0.8375 x = 1.183810057 + -0.8375 Combine like terms: 1.183810057 + -0.8375 = 0.346310057 x = 0.346310057 Simplifying x = 0.346310057Subproblem 2
x + 0.8375 = -1.183810057 Simplifying x + 0.8375 = -1.183810057 Reorder the terms: 0.8375 + x = -1.183810057 Solving 0.8375 + x = -1.183810057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8375' to each side of the equation. 0.8375 + -0.8375 + x = -1.183810057 + -0.8375 Combine like terms: 0.8375 + -0.8375 = 0.0000 0.0000 + x = -1.183810057 + -0.8375 x = -1.183810057 + -0.8375 Combine like terms: -1.183810057 + -0.8375 = -2.021310057 x = -2.021310057 Simplifying x = -2.021310057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.346310057, -2.021310057}
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