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Simplifying 5 + -2(3x2 + 2x) = x2 + 7 + -2x2 Reorder the terms: 5 + -2(2x + 3x2) = x2 + 7 + -2x2 5 + (2x * -2 + 3x2 * -2) = x2 + 7 + -2x2 5 + (-4x + -6x2) = x2 + 7 + -2x2 Reorder the terms: 5 + -4x + -6x2 = 7 + x2 + -2x2 Combine like terms: x2 + -2x2 = -1x2 5 + -4x + -6x2 = 7 + -1x2 Solving 5 + -4x + -6x2 = 7 + -1x2 Solving for variable 'x'. Reorder the terms: 5 + -7 + -4x + -6x2 + x2 = 7 + -1x2 + -7 + x2 Combine like terms: 5 + -7 = -2 -2 + -4x + -6x2 + x2 = 7 + -1x2 + -7 + x2 Combine like terms: -6x2 + x2 = -5x2 -2 + -4x + -5x2 = 7 + -1x2 + -7 + x2 Reorder the terms: -2 + -4x + -5x2 = 7 + -7 + -1x2 + x2 Combine like terms: 7 + -7 = 0 -2 + -4x + -5x2 = 0 + -1x2 + x2 -2 + -4x + -5x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -2 + -4x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 4x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + 4x + 5x2 = 0 Solving 2 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 0.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.8x + x2 = 0 + -0.4 0.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 0.8x + x2 = -0.4 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = -0.4 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -0.4 + 0.16 Combine like terms: -0.4 + 0.16 = -0.24 0.16 + 0.8x + x2 = -0.24 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = -0.24 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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