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Simplifying 5(3x + 4) * 2x = 7x + -3(-2x + 11) Reorder the terms: 5(4 + 3x) * 2x = 7x + -3(-2x + 11) Reorder the terms for easier multiplication: 5 * 2x(4 + 3x) = 7x + -3(-2x + 11) Multiply 5 * 2 10x(4 + 3x) = 7x + -3(-2x + 11) (4 * 10x + 3x * 10x) = 7x + -3(-2x + 11) (40x + 30x2) = 7x + -3(-2x + 11) Reorder the terms: 40x + 30x2 = 7x + -3(11 + -2x) 40x + 30x2 = 7x + (11 * -3 + -2x * -3) 40x + 30x2 = 7x + (-33 + 6x) Reorder the terms: 40x + 30x2 = -33 + 7x + 6x Combine like terms: 7x + 6x = 13x 40x + 30x2 = -33 + 13x Solving 40x + 30x2 = -33 + 13x Solving for variable 'x'. Reorder the terms: 33 + 40x + -13x + 30x2 = -33 + 13x + 33 + -13x Combine like terms: 40x + -13x = 27x 33 + 27x + 30x2 = -33 + 13x + 33 + -13x Reorder the terms: 33 + 27x + 30x2 = -33 + 33 + 13x + -13x Combine like terms: -33 + 33 = 0 33 + 27x + 30x2 = 0 + 13x + -13x 33 + 27x + 30x2 = 13x + -13x Combine like terms: 13x + -13x = 0 33 + 27x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(11 + 9x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + 9x + 10x2)' equal to zero and attempt to solve: Simplifying 11 + 9x + 10x2 = 0 Solving 11 + 9x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.1 + 0.9x + x2 = 0.0 Move the constant term to the right: Add '-1.1' to each side of the equation. 1.1 + 0.9x + -1.1 + x2 = 0.0 + -1.1 Reorder the terms: 1.1 + -1.1 + 0.9x + x2 = 0.0 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + 0.9x + x2 = 0.0 + -1.1 0.9x + x2 = 0.0 + -1.1 Combine like terms: 0.0 + -1.1 = -1.1 0.9x + x2 = -1.1 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = -1.1 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = -1.1 + 0.2025 Combine like terms: -1.1 + 0.2025 = -0.8975 0.2025 + 0.9x + x2 = -0.8975 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = -0.8975 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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