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Simplifying 87x2 + -42 = 121x Reorder the terms: -42 + 87x2 = 121x Solving -42 + 87x2 = 121x Solving for variable 'x'. Reorder the terms: -42 + -121x + 87x2 = 121x + -121x Combine like terms: 121x + -121x = 0 -42 + -121x + 87x2 = 0 Begin completing the square. Divide all terms by 87 the coefficient of the squared term: Divide each side by '87'. -0.4827586207 + -1.390804598x + x2 = 0 Move the constant term to the right: Add '0.4827586207' to each side of the equation. -0.4827586207 + -1.390804598x + 0.4827586207 + x2 = 0 + 0.4827586207 Reorder the terms: -0.4827586207 + 0.4827586207 + -1.390804598x + x2 = 0 + 0.4827586207 Combine like terms: -0.4827586207 + 0.4827586207 = 0.0000000000 0.0000000000 + -1.390804598x + x2 = 0 + 0.4827586207 -1.390804598x + x2 = 0 + 0.4827586207 Combine like terms: 0 + 0.4827586207 = 0.4827586207 -1.390804598x + x2 = 0.4827586207 The x term is -1.390804598x. Take half its coefficient (-0.695402299). Square it (0.4835843575) and add it to both sides. Add '0.4835843575' to each side of the equation. -1.390804598x + 0.4835843575 + x2 = 0.4827586207 + 0.4835843575 Reorder the terms: 0.4835843575 + -1.390804598x + x2 = 0.4827586207 + 0.4835843575 Combine like terms: 0.4827586207 + 0.4835843575 = 0.9663429782 0.4835843575 + -1.390804598x + x2 = 0.9663429782 Factor a perfect square on the left side: (x + -0.695402299)(x + -0.695402299) = 0.9663429782 Calculate the square root of the right side: 0.983027455 Break this problem into two subproblems by setting (x + -0.695402299) equal to 0.983027455 and -0.983027455.Subproblem 1
x + -0.695402299 = 0.983027455 Simplifying x + -0.695402299 = 0.983027455 Reorder the terms: -0.695402299 + x = 0.983027455 Solving -0.695402299 + x = 0.983027455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.695402299' to each side of the equation. -0.695402299 + 0.695402299 + x = 0.983027455 + 0.695402299 Combine like terms: -0.695402299 + 0.695402299 = 0.000000000 0.000000000 + x = 0.983027455 + 0.695402299 x = 0.983027455 + 0.695402299 Combine like terms: 0.983027455 + 0.695402299 = 1.678429754 x = 1.678429754 Simplifying x = 1.678429754Subproblem 2
x + -0.695402299 = -0.983027455 Simplifying x + -0.695402299 = -0.983027455 Reorder the terms: -0.695402299 + x = -0.983027455 Solving -0.695402299 + x = -0.983027455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.695402299' to each side of the equation. -0.695402299 + 0.695402299 + x = -0.983027455 + 0.695402299 Combine like terms: -0.695402299 + 0.695402299 = 0.000000000 0.000000000 + x = -0.983027455 + 0.695402299 x = -0.983027455 + 0.695402299 Combine like terms: -0.983027455 + 0.695402299 = -0.287625156 x = -0.287625156 Simplifying x = -0.287625156Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.678429754, -0.287625156}
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