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Simplifying x2 + 3x + -10(x + 5) = x2 + kx + 30 Reorder the terms: x2 + 3x + -10(5 + x) = x2 + kx + 30 x2 + 3x + (5 * -10 + x * -10) = x2 + kx + 30 x2 + 3x + (-50 + -10x) = x2 + kx + 30 Reorder the terms: -50 + 3x + -10x + x2 = x2 + kx + 30 Combine like terms: 3x + -10x = -7x -50 + -7x + x2 = x2 + kx + 30 Reorder the terms: -50 + -7x + x2 = 30 + kx + x2 Add '-1x2' to each side of the equation. -50 + -7x + x2 + -1x2 = 30 + kx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + -7x + 0 = 30 + kx + x2 + -1x2 -50 + -7x = 30 + kx + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -50 + -7x = 30 + kx + 0 -50 + -7x = 30 + kx Solving -50 + -7x = 30 + kx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1kx' to each side of the equation. -50 + -1kx + -7x = 30 + kx + -1kx Combine like terms: kx + -1kx = 0 -50 + -1kx + -7x = 30 + 0 -50 + -1kx + -7x = 30 Add '50' to each side of the equation. -50 + -1kx + 50 + -7x = 30 + 50 Reorder the terms: -50 + 50 + -1kx + -7x = 30 + 50 Combine like terms: -50 + 50 = 0 0 + -1kx + -7x = 30 + 50 -1kx + -7x = 30 + 50 Combine like terms: 30 + 50 = 80 -1kx + -7x = 80 Reorder the terms: -80 + -1kx + -7x = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -1kx + -7x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(80 + kx + 7x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(80 + kx + 7x)' equal to zero and attempt to solve: Simplifying 80 + kx + 7x = 0 Solving 80 + kx + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-80' to each side of the equation. 80 + kx + -80 + 7x = 0 + -80 Reorder the terms: 80 + -80 + kx + 7x = 0 + -80 Combine like terms: 80 + -80 = 0 0 + kx + 7x = 0 + -80 kx + 7x = 0 + -80 Combine like terms: 0 + -80 = -80 kx + 7x = -80 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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