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Simplifying 7x(-8 + -1x + 7) = 100 Reorder the terms: 7x(-8 + 7 + -1x) = 100 Combine like terms: -8 + 7 = -1 7x(-1 + -1x) = 100 (-1 * 7x + -1x * 7x) = 100 (-7x + -7x2) = 100 Solving -7x + -7x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + -7x + -7x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -7x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(100 + 7x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(100 + 7x + 7x2)' equal to zero and attempt to solve: Simplifying 100 + 7x + 7x2 = 0 Solving 100 + 7x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 14.28571429 + x + x2 = 0 Move the constant term to the right: Add '-14.28571429' to each side of the equation. 14.28571429 + x + -14.28571429 + x2 = 0 + -14.28571429 Reorder the terms: 14.28571429 + -14.28571429 + x + x2 = 0 + -14.28571429 Combine like terms: 14.28571429 + -14.28571429 = 0.00000000 0.00000000 + x + x2 = 0 + -14.28571429 x + x2 = 0 + -14.28571429 Combine like terms: 0 + -14.28571429 = -14.28571429 x + x2 = -14.28571429 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -14.28571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -14.28571429 + 0.25 Combine like terms: -14.28571429 + 0.25 = -14.03571429 1.25 + x2 = -14.03571429 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -14.03571429 Can't calculate square root of the right side. 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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