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Simplifying x(x + -8) = 1.75 Reorder the terms: x(-8 + x) = 1.75 (-8 * x + x * x) = 1.75 (-8x + x2) = 1.75 Solving -8x + x2 = 1.75 Solving for variable 'x'. Reorder the terms: -1.75 + -8x + x2 = 1.75 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 -1.75 + -8x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -8x + 1.75 + x2 = 0.00 + 1.75 Reorder the terms: -1.75 + 1.75 + -8x + x2 = 0.00 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -8x + x2 = 0.00 + 1.75 -8x + x2 = 0.00 + 1.75 Combine like terms: 0.00 + 1.75 = 1.75 -8x + x2 = 1.75 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1.75 + 16 Reorder the terms: 16 + -8x + x2 = 1.75 + 16 Combine like terms: 1.75 + 16 = 17.75 16 + -8x + x2 = 17.75 Factor a perfect square on the left side: (x + -4)(x + -4) = 17.75 Calculate the square root of the right side: 4.213074887 Break this problem into two subproblems by setting (x + -4) equal to 4.213074887 and -4.213074887.Subproblem 1
x + -4 = 4.213074887 Simplifying x + -4 = 4.213074887 Reorder the terms: -4 + x = 4.213074887 Solving -4 + x = 4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.213074887 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.213074887 + 4 x = 4.213074887 + 4 Combine like terms: 4.213074887 + 4 = 8.213074887 x = 8.213074887 Simplifying x = 8.213074887Subproblem 2
x + -4 = -4.213074887 Simplifying x + -4 = -4.213074887 Reorder the terms: -4 + x = -4.213074887 Solving -4 + x = -4.213074887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.213074887 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.213074887 + 4 x = -4.213074887 + 4 Combine like terms: -4.213074887 + 4 = -0.213074887 x = -0.213074887 Simplifying x = -0.213074887Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.213074887, -0.213074887}
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