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Simplifying (2x2 + -5x + -7) + -1(7x2 + 3) = x Reorder the terms: (-7 + -5x + 2x2) + -1(7x2 + 3) = x Remove parenthesis around (-7 + -5x + 2x2) -7 + -5x + 2x2 + -1(7x2 + 3) = x Reorder the terms: -7 + -5x + 2x2 + -1(3 + 7x2) = x -7 + -5x + 2x2 + (3 * -1 + 7x2 * -1) = x -7 + -5x + 2x2 + (-3 + -7x2) = x Reorder the terms: -7 + -3 + -5x + 2x2 + -7x2 = x Combine like terms: -7 + -3 = -10 -10 + -5x + 2x2 + -7x2 = x Combine like terms: 2x2 + -7x2 = -5x2 -10 + -5x + -5x2 = x Solving -10 + -5x + -5x2 = x Solving for variable 'x'. Reorder the terms: -10 + -5x + -1x + -5x2 = x + -1x Combine like terms: -5x + -1x = -6x -10 + -6x + -5x2 = x + -1x Combine like terms: x + -1x = 0 -10 + -6x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 6x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + 6x + 5x2 = 0 Solving 10 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 1.2x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 1.2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 1.2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1.2x + x2 = 0 + -2 1.2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 1.2x + x2 = -2 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -2 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -2 + 0.36 Combine like terms: -2 + 0.36 = -1.64 0.36 + 1.2x + x2 = -1.64 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = -1.64 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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