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Simplifying 10x2 + 8x + 160 = 90 Reorder the terms: 160 + 8x + 10x2 = 90 Solving 160 + 8x + 10x2 = 90 Solving for variable 'x'. Reorder the terms: 160 + -90 + 8x + 10x2 = 90 + -90 Combine like terms: 160 + -90 = 70 70 + 8x + 10x2 = 90 + -90 Combine like terms: 90 + -90 = 0 70 + 8x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(35 + 4x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying 35 + 4x + 5x2 = 0 Solving 35 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 7 + 0.8x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 0.8x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 0.8x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 0.8x + x2 = 0 + -7 0.8x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 0.8x + x2 = -7 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 = -7 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -7 + 0.16 Combine like terms: -7 + 0.16 = -6.84 0.16 + 0.8x + x2 = -6.84 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = -6.84 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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