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Simplifying m(0) = 4x2 + 10x + 19 Reorder the terms for easier multiplication: 0m = 4x2 + 10x + 19 Anything times zero is zero. 0m = 4x2 + 10x + 19 Reorder the terms: 0 = 19 + 10x + 4x2 Solving 0 = 19 + 10x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -19 = -19 -19 + -10x + -4x2 = 19 + 10x + 4x2 + -19 + -10x + -4x2 Reorder the terms: -19 + -10x + -4x2 = 19 + -19 + 10x + -10x + 4x2 + -4x2 Combine like terms: 19 + -19 = 0 -19 + -10x + -4x2 = 0 + 10x + -10x + 4x2 + -4x2 -19 + -10x + -4x2 = 10x + -10x + 4x2 + -4x2 Combine like terms: 10x + -10x = 0 -19 + -10x + -4x2 = 0 + 4x2 + -4x2 -19 + -10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -19 + -10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(19 + 10x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(19 + 10x + 4x2)' equal to zero and attempt to solve: Simplifying 19 + 10x + 4x2 = 0 Solving 19 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '-4.75' to each side of the equation. 4.75 + 2.5x + -4.75 + x2 = 0 + -4.75 Reorder the terms: 4.75 + -4.75 + 2.5x + x2 = 0 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + 2.5x + x2 = 0 + -4.75 2.5x + x2 = 0 + -4.75 Combine like terms: 0 + -4.75 = -4.75 2.5x + x2 = -4.75 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 = -4.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -4.75 + 1.5625 Combine like terms: -4.75 + 1.5625 = -3.1875 1.5625 + 2.5x + x2 = -3.1875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -3.1875 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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