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Simplifying 16x2 + -7x + -40 = 0 Reorder the terms: -40 + -7x + 16x2 = 0 Solving -40 + -7x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.5 + -0.4375x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -0.4375x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -0.4375x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -0.4375x + x2 = 0 + 2.5 -0.4375x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -0.4375x + x2 = 2.5 The x term is -0.4375x. Take half its coefficient (-0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. -0.4375x + 0.0478515625 + x2 = 2.5 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375x + x2 = 2.5 + 0.0478515625 Combine like terms: 2.5 + 0.0478515625 = 2.5478515625 0.0478515625 + -0.4375x + x2 = 2.5478515625 Factor a perfect square on the left side: (x + -0.21875)(x + -0.21875) = 2.5478515625 Calculate the square root of the right side: 1.596199099 Break this problem into two subproblems by setting (x + -0.21875) equal to 1.596199099 and -1.596199099.Subproblem 1
x + -0.21875 = 1.596199099 Simplifying x + -0.21875 = 1.596199099 Reorder the terms: -0.21875 + x = 1.596199099 Solving -0.21875 + x = 1.596199099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + x = 1.596199099 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + x = 1.596199099 + 0.21875 x = 1.596199099 + 0.21875 Combine like terms: 1.596199099 + 0.21875 = 1.814949099 x = 1.814949099 Simplifying x = 1.814949099Subproblem 2
x + -0.21875 = -1.596199099 Simplifying x + -0.21875 = -1.596199099 Reorder the terms: -0.21875 + x = -1.596199099 Solving -0.21875 + x = -1.596199099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + x = -1.596199099 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + x = -1.596199099 + 0.21875 x = -1.596199099 + 0.21875 Combine like terms: -1.596199099 + 0.21875 = -1.377449099 x = -1.377449099 Simplifying x = -1.377449099Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.814949099, -1.377449099}
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