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Simplifying -5x2 + 7x + 8 = 0 Reorder the terms: 8 + 7x + -5x2 = 0 Solving 8 + 7x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.6 + -1.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -1.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -1.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -1.4x + x2 = 0 + 1.6 -1.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -1.4x + x2 = 1.6 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 1.6 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 1.6 + 0.49 Combine like terms: 1.6 + 0.49 = 2.09 0.49 + -1.4x + x2 = 2.09 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (x + -0.7) equal to 1.445683229 and -1.445683229.Subproblem 1
x + -0.7 = 1.445683229 Simplifying x + -0.7 = 1.445683229 Reorder the terms: -0.7 + x = 1.445683229 Solving -0.7 + x = 1.445683229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 1.445683229 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 1.445683229 + 0.7 x = 1.445683229 + 0.7 Combine like terms: 1.445683229 + 0.7 = 2.145683229 x = 2.145683229 Simplifying x = 2.145683229Subproblem 2
x + -0.7 = -1.445683229 Simplifying x + -0.7 = -1.445683229 Reorder the terms: -0.7 + x = -1.445683229 Solving -0.7 + x = -1.445683229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -1.445683229 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -1.445683229 + 0.7 x = -1.445683229 + 0.7 Combine like terms: -1.445683229 + 0.7 = -0.745683229 x = -0.745683229 Simplifying x = -0.745683229Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.145683229, -0.745683229}
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