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Simplifying 3(4x2 + -5) + -2(x2 + 3x) = 0 Reorder the terms: 3(-5 + 4x2) + -2(x2 + 3x) = 0 (-5 * 3 + 4x2 * 3) + -2(x2 + 3x) = 0 (-15 + 12x2) + -2(x2 + 3x) = 0 Reorder the terms: -15 + 12x2 + -2(3x + x2) = 0 -15 + 12x2 + (3x * -2 + x2 * -2) = 0 -15 + 12x2 + (-6x + -2x2) = 0 Reorder the terms: -15 + -6x + 12x2 + -2x2 = 0 Combine like terms: 12x2 + -2x2 = 10x2 -15 + -6x + 10x2 = 0 Solving -15 + -6x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.5 + -0.6x + x2 = 0.0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.6x + 1.5 + x2 = 0.0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.6x + x2 = 0.0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.6x + x2 = 0.0 + 1.5 -0.6x + x2 = 0.0 + 1.5 Combine like terms: 0.0 + 1.5 = 1.5 -0.6x + x2 = 1.5 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 1.5 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 1.5 + 0.09 Combine like terms: 1.5 + 0.09 = 1.59 0.09 + -0.6x + x2 = 1.59 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 1.59 Calculate the square root of the right side: 1.260952021 Break this problem into two subproblems by setting (x + -0.3) equal to 1.260952021 and -1.260952021.Subproblem 1
x + -0.3 = 1.260952021 Simplifying x + -0.3 = 1.260952021 Reorder the terms: -0.3 + x = 1.260952021 Solving -0.3 + x = 1.260952021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 1.260952021 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 1.260952021 + 0.3 x = 1.260952021 + 0.3 Combine like terms: 1.260952021 + 0.3 = 1.560952021 x = 1.560952021 Simplifying x = 1.560952021Subproblem 2
x + -0.3 = -1.260952021 Simplifying x + -0.3 = -1.260952021 Reorder the terms: -0.3 + x = -1.260952021 Solving -0.3 + x = -1.260952021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -1.260952021 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -1.260952021 + 0.3 x = -1.260952021 + 0.3 Combine like terms: -1.260952021 + 0.3 = -0.960952021 x = -0.960952021 Simplifying x = -0.960952021Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.560952021, -0.960952021}
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