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Simplifying 10x2 + -6 = 14x2 + 10x + 50 Reorder the terms: -6 + 10x2 = 14x2 + 10x + 50 Reorder the terms: -6 + 10x2 = 50 + 10x + 14x2 Solving -6 + 10x2 = 50 + 10x + 14x2 Solving for variable 'x'. Reorder the terms: -6 + -50 + -10x + 10x2 + -14x2 = 50 + 10x + 14x2 + -50 + -10x + -14x2 Combine like terms: -6 + -50 = -56 -56 + -10x + 10x2 + -14x2 = 50 + 10x + 14x2 + -50 + -10x + -14x2 Combine like terms: 10x2 + -14x2 = -4x2 -56 + -10x + -4x2 = 50 + 10x + 14x2 + -50 + -10x + -14x2 Reorder the terms: -56 + -10x + -4x2 = 50 + -50 + 10x + -10x + 14x2 + -14x2 Combine like terms: 50 + -50 = 0 -56 + -10x + -4x2 = 0 + 10x + -10x + 14x2 + -14x2 -56 + -10x + -4x2 = 10x + -10x + 14x2 + -14x2 Combine like terms: 10x + -10x = 0 -56 + -10x + -4x2 = 0 + 14x2 + -14x2 -56 + -10x + -4x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -56 + -10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(28 + 5x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(28 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 28 + 5x + 2x2 = 0 Solving 28 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14 + 2.5x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + 2.5x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + 2.5x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 2.5x + x2 = 0 + -14 2.5x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 2.5x + x2 = -14 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -14 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -14 + 1.5625 Combine like terms: -14 + 1.5625 = -12.4375 1.5625 + 2.5x + x2 = -12.4375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -12.4375 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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