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Simplifying -7x + 5 + -7(5x2 + 3) + 10x2 = 0 Reorder the terms: -7x + 5 + -7(3 + 5x2) + 10x2 = 0 -7x + 5 + (3 * -7 + 5x2 * -7) + 10x2 = 0 -7x + 5 + (-21 + -35x2) + 10x2 = 0 Reorder the terms: 5 + -21 + -7x + -35x2 + 10x2 = 0 Combine like terms: 5 + -21 = -16 -16 + -7x + -35x2 + 10x2 = 0 Combine like terms: -35x2 + 10x2 = -25x2 -16 + -7x + -25x2 = 0 Solving -16 + -7x + -25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 7x + 25x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 7x + 25x2)' equal to zero and attempt to solve: Simplifying 16 + 7x + 25x2 = 0 Solving 16 + 7x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.64 + 0.28x + x2 = 0 Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + 0.28x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + 0.28x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + 0.28x + x2 = 0 + -0.64 0.28x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 0.28x + x2 = -0.64 The x term is 0.28x. Take half its coefficient (0.14). Square it (0.0196) and add it to both sides. Add '0.0196' to each side of the equation. 0.28x + 0.0196 + x2 = -0.64 + 0.0196 Reorder the terms: 0.0196 + 0.28x + x2 = -0.64 + 0.0196 Combine like terms: -0.64 + 0.0196 = -0.6204 0.0196 + 0.28x + x2 = -0.6204 Factor a perfect square on the left side: (x + 0.14)(x + 0.14) = -0.6204 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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