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Simplifying (0.43 + -1x)(0.87 + -1x) = 24.2x Multiply (0.43 + -1x) * (0.87 + -1x) (0.43(0.87 + -1x) + -1x * (0.87 + -1x)) = 24.2x ((0.87 * 0.43 + -1x * 0.43) + -1x * (0.87 + -1x)) = 24.2x ((0.3741 + -0.43x) + -1x * (0.87 + -1x)) = 24.2x (0.3741 + -0.43x + (0.87 * -1x + -1x * -1x)) = 24.2x (0.3741 + -0.43x + (-0.87x + 1x2)) = 24.2x Combine like terms: -0.43x + -0.87x = -1.3x (0.3741 + -1.3x + 1x2) = 24.2x Solving 0.3741 + -1.3x + 1x2 = 24.2x Solving for variable 'x'. Reorder the terms: 0.3741 + -1.3x + -24.2x + 1x2 = 24.2x + -24.2x Combine like terms: -1.3x + -24.2x = -25.5x 0.3741 + -25.5x + 1x2 = 24.2x + -24.2x Combine like terms: 24.2x + -24.2x = 0.0 0.3741 + -25.5x + 1x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-0.3741' to each side of the equation. 0.3741 + -25.5x + -0.3741 + x2 = 0.0 + -0.3741 Reorder the terms: 0.3741 + -0.3741 + -25.5x + x2 = 0.0 + -0.3741 Combine like terms: 0.3741 + -0.3741 = 0.0000 0.0000 + -25.5x + x2 = 0.0 + -0.3741 -25.5x + x2 = 0.0 + -0.3741 Combine like terms: 0.0 + -0.3741 = -0.3741 -25.5x + x2 = -0.3741 The x term is -25.5x. Take half its coefficient (-12.75). Square it (162.5625) and add it to both sides. Add '162.5625' to each side of the equation. -25.5x + 162.5625 + x2 = -0.3741 + 162.5625 Reorder the terms: 162.5625 + -25.5x + x2 = -0.3741 + 162.5625 Combine like terms: -0.3741 + 162.5625 = 162.1884 162.5625 + -25.5x + x2 = 162.1884 Factor a perfect square on the left side: (x + -12.75)(x + -12.75) = 162.1884 Calculate the square root of the right side: 12.735320962 Break this problem into two subproblems by setting (x + -12.75) equal to 12.735320962 and -12.735320962.Subproblem 1
x + -12.75 = 12.735320962 Simplifying x + -12.75 = 12.735320962 Reorder the terms: -12.75 + x = 12.735320962 Solving -12.75 + x = 12.735320962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = 12.735320962 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = 12.735320962 + 12.75 x = 12.735320962 + 12.75 Combine like terms: 12.735320962 + 12.75 = 25.485320962 x = 25.485320962 Simplifying x = 25.485320962Subproblem 2
x + -12.75 = -12.735320962 Simplifying x + -12.75 = -12.735320962 Reorder the terms: -12.75 + x = -12.735320962 Solving -12.75 + x = -12.735320962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.75' to each side of the equation. -12.75 + 12.75 + x = -12.735320962 + 12.75 Combine like terms: -12.75 + 12.75 = 0.00 0.00 + x = -12.735320962 + 12.75 x = -12.735320962 + 12.75 Combine like terms: -12.735320962 + 12.75 = 0.014679038 x = 0.014679038 Simplifying x = 0.014679038Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.485320962, 0.014679038}
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