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Simplifying 5x + -7x(x + 3) = -2x + 12 Reorder the terms: 5x + -7x(3 + x) = -2x + 12 5x + (3 * -7x + x * -7x) = -2x + 12 5x + (-21x + -7x2) = -2x + 12 Combine like terms: 5x + -21x = -16x -16x + -7x2 = -2x + 12 Reorder the terms: -16x + -7x2 = 12 + -2x Solving -16x + -7x2 = 12 + -2x Solving for variable 'x'. Reorder the terms: -12 + -16x + 2x + -7x2 = 12 + -2x + -12 + 2x Combine like terms: -16x + 2x = -14x -12 + -14x + -7x2 = 12 + -2x + -12 + 2x Reorder the terms: -12 + -14x + -7x2 = 12 + -12 + -2x + 2x Combine like terms: 12 + -12 = 0 -12 + -14x + -7x2 = 0 + -2x + 2x -12 + -14x + -7x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -12 + -14x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 14x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 14x + 7x2)' equal to zero and attempt to solve: Simplifying 12 + 14x + 7x2 = 0 Solving 12 + 14x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.714285714 + 2x + x2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + 2x + -1.714285714 + x2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + 2x + x2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + 2x + x2 = 0 + -1.714285714 2x + x2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 2x + x2 = -1.714285714 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -1.714285714 + 1 Reorder the terms: 1 + 2x + x2 = -1.714285714 + 1 Combine like terms: -1.714285714 + 1 = -0.714285714 1 + 2x + x2 = -0.714285714 Factor a perfect square on the left side: (x + 1)(x + 1) = -0.714285714 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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