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Simplifying (x + h)(x + h) + -1x2 = 0 Reorder the terms: (h + x)(x + h) + -1x2 = 0 Reorder the terms: (h + x)(h + x) + -1x2 = 0 Multiply (h + x) * (h + x) (h(h + x) + x(h + x)) + -1x2 = 0 ((h * h + x * h) + x(h + x)) + -1x2 = 0 Reorder the terms: ((hx + h2) + x(h + x)) + -1x2 = 0 ((hx + h2) + x(h + x)) + -1x2 = 0 (hx + h2 + (h * x + x * x)) + -1x2 = 0 (hx + h2 + (hx + x2)) + -1x2 = 0 Reorder the terms: (hx + hx + h2 + x2) + -1x2 = 0 Combine like terms: hx + hx = 2hx (2hx + h2 + x2) + -1x2 = 0 Combine like terms: x2 + -1x2 = 0 2hx + h2 + 0 = 0 2hx + h2 = 0 Solving 2hx + h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), 'h'. h(2x + h) = 0Subproblem 1
Set the factor 'h' equal to zero and attempt to solve: Simplifying h = 0 Solving h = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h = 0Subproblem 2
Set the factor '(2x + h)' equal to zero and attempt to solve: Simplifying 2x + h = 0 Reorder the terms: h + 2x = 0 Solving h + 2x = 0 Move all terms containing h to the left, all other terms to the right. Add '-2x' to each side of the equation. h + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 h + 0 = 0 + -2x h = 0 + -2x Remove the zero: h = -2x Simplifying h = -2xSolution
h = {0, -2x}
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