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Simplifying 2(x + -5) + 3 = 4x2 + 93 Reorder the terms: 2(-5 + x) + 3 = 4x2 + 93 (-5 * 2 + x * 2) + 3 = 4x2 + 93 (-10 + 2x) + 3 = 4x2 + 93 Reorder the terms: -10 + 3 + 2x = 4x2 + 93 Combine like terms: -10 + 3 = -7 -7 + 2x = 4x2 + 93 Reorder the terms: -7 + 2x = 93 + 4x2 Solving -7 + 2x = 93 + 4x2 Solving for variable 'x'. Reorder the terms: -7 + -93 + 2x + -4x2 = 93 + 4x2 + -93 + -4x2 Combine like terms: -7 + -93 = -100 -100 + 2x + -4x2 = 93 + 4x2 + -93 + -4x2 Reorder the terms: -100 + 2x + -4x2 = 93 + -93 + 4x2 + -4x2 Combine like terms: 93 + -93 = 0 -100 + 2x + -4x2 = 0 + 4x2 + -4x2 -100 + 2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -100 + 2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + x + -2x2)' equal to zero and attempt to solve: Simplifying -50 + x + -2x2 = 0 Solving -50 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 25 + -0.5x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -0.5x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -0.5x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -0.5x + x2 = 0 + -25 -0.5x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -0.5x + x2 = -25 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. -0.5x + 0.25 + x2 = -25 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -25 + 0.25 Combine like terms: -25 + 0.25 = -24.75 0.25 + -0.5x + x2 = -24.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -24.75 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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