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Simplifying -4x2 + 5x + 7 = 0 Reorder the terms: 7 + 5x + -4x2 = 0 Solving 7 + 5x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -1.25x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -1.25x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -1.25x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -1.25x + x2 = 0 + 1.75 -1.25x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -1.25x + x2 = 1.75 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 1.75 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 1.75 + 0.390625 Combine like terms: 1.75 + 0.390625 = 2.140625 0.390625 + -1.25x + x2 = 2.140625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (x + -0.625) equal to 1.463087489 and -1.463087489.Subproblem 1
x + -0.625 = 1.463087489 Simplifying x + -0.625 = 1.463087489 Reorder the terms: -0.625 + x = 1.463087489 Solving -0.625 + x = 1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 1.463087489 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 1.463087489 + 0.625 x = 1.463087489 + 0.625 Combine like terms: 1.463087489 + 0.625 = 2.088087489 x = 2.088087489 Simplifying x = 2.088087489Subproblem 2
x + -0.625 = -1.463087489 Simplifying x + -0.625 = -1.463087489 Reorder the terms: -0.625 + x = -1.463087489 Solving -0.625 + x = -1.463087489 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -1.463087489 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -1.463087489 + 0.625 x = -1.463087489 + 0.625 Combine like terms: -1.463087489 + 0.625 = -0.838087489 x = -0.838087489 Simplifying x = -0.838087489Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.088087489, -0.838087489}
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