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Simplifying 4(x2 + 3) + -5x(x + 3) = 0 Reorder the terms: 4(3 + x2) + -5x(x + 3) = 0 (3 * 4 + x2 * 4) + -5x(x + 3) = 0 (12 + 4x2) + -5x(x + 3) = 0 Reorder the terms: 12 + 4x2 + -5x(3 + x) = 0 12 + 4x2 + (3 * -5x + x * -5x) = 0 12 + 4x2 + (-15x + -5x2) = 0 Reorder the terms: 12 + -15x + 4x2 + -5x2 = 0 Combine like terms: 4x2 + -5x2 = -1x2 12 + -15x + -1x2 = 0 Solving 12 + -15x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + 15x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 15x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 15x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 15x + x2 = 0 + 12 15x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 15x + x2 = 12 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 12 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 12 + 56.25 Combine like terms: 12 + 56.25 = 68.25 56.25 + 15x + x2 = 68.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 7.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 7.5 = 8.261355821 Simplifying x + 7.5 = 8.261355821 Reorder the terms: 7.5 + x = 8.261355821 Solving 7.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.261355821 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.261355821 + -7.5 x = 8.261355821 + -7.5 Combine like terms: 8.261355821 + -7.5 = 0.761355821 x = 0.761355821 Simplifying x = 0.761355821Subproblem 2
x + 7.5 = -8.261355821 Simplifying x + 7.5 = -8.261355821 Reorder the terms: 7.5 + x = -8.261355821 Solving 7.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.261355821 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.261355821 + -7.5 x = -8.261355821 + -7.5 Combine like terms: -8.261355821 + -7.5 = -15.761355821 x = -15.761355821 Simplifying x = -15.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.761355821, -15.761355821}
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