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Simplifying -7 = x + 8(x2 + -6x + -7) Reorder the terms: -7 = x + 8(-7 + -6x + x2) -7 = x + (-7 * 8 + -6x * 8 + x2 * 8) -7 = x + (-56 + -48x + 8x2) Reorder the terms: -7 = -56 + x + -48x + 8x2 Combine like terms: x + -48x = -47x -7 = -56 + -47x + 8x2 Solving -7 = -56 + -47x + 8x2 Solving for variable 'x'. Combine like terms: -7 + 56 = 49 49 + 47x + -8x2 = -56 + -47x + 8x2 + 56 + 47x + -8x2 Reorder the terms: 49 + 47x + -8x2 = -56 + 56 + -47x + 47x + 8x2 + -8x2 Combine like terms: -56 + 56 = 0 49 + 47x + -8x2 = 0 + -47x + 47x + 8x2 + -8x2 49 + 47x + -8x2 = -47x + 47x + 8x2 + -8x2 Combine like terms: -47x + 47x = 0 49 + 47x + -8x2 = 0 + 8x2 + -8x2 49 + 47x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 49 + 47x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.125 + -5.875x + x2 = 0 Move the constant term to the right: Add '6.125' to each side of the equation. -6.125 + -5.875x + 6.125 + x2 = 0 + 6.125 Reorder the terms: -6.125 + 6.125 + -5.875x + x2 = 0 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + -5.875x + x2 = 0 + 6.125 -5.875x + x2 = 0 + 6.125 Combine like terms: 0 + 6.125 = 6.125 -5.875x + x2 = 6.125 The x term is -5.875x. Take half its coefficient (-2.9375). Square it (8.62890625) and add it to both sides. Add '8.62890625' to each side of the equation. -5.875x + 8.62890625 + x2 = 6.125 + 8.62890625 Reorder the terms: 8.62890625 + -5.875x + x2 = 6.125 + 8.62890625 Combine like terms: 6.125 + 8.62890625 = 14.75390625 8.62890625 + -5.875x + x2 = 14.75390625 Factor a perfect square on the left side: (x + -2.9375)(x + -2.9375) = 14.75390625 Calculate the square root of the right side: 3.841081391 Break this problem into two subproblems by setting (x + -2.9375) equal to 3.841081391 and -3.841081391.Subproblem 1
x + -2.9375 = 3.841081391 Simplifying x + -2.9375 = 3.841081391 Reorder the terms: -2.9375 + x = 3.841081391 Solving -2.9375 + x = 3.841081391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = 3.841081391 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = 3.841081391 + 2.9375 x = 3.841081391 + 2.9375 Combine like terms: 3.841081391 + 2.9375 = 6.778581391 x = 6.778581391 Simplifying x = 6.778581391Subproblem 2
x + -2.9375 = -3.841081391 Simplifying x + -2.9375 = -3.841081391 Reorder the terms: -2.9375 + x = -3.841081391 Solving -2.9375 + x = -3.841081391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9375' to each side of the equation. -2.9375 + 2.9375 + x = -3.841081391 + 2.9375 Combine like terms: -2.9375 + 2.9375 = 0.0000 0.0000 + x = -3.841081391 + 2.9375 x = -3.841081391 + 2.9375 Combine like terms: -3.841081391 + 2.9375 = -0.903581391 x = -0.903581391 Simplifying x = -0.903581391Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.778581391, -0.903581391}
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