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Simplifying 2(x2 + -3x + 4) + -3x(5x + -4) = 0 Reorder the terms: 2(4 + -3x + x2) + -3x(5x + -4) = 0 (4 * 2 + -3x * 2 + x2 * 2) + -3x(5x + -4) = 0 (8 + -6x + 2x2) + -3x(5x + -4) = 0 Reorder the terms: 8 + -6x + 2x2 + -3x(-4 + 5x) = 0 8 + -6x + 2x2 + (-4 * -3x + 5x * -3x) = 0 8 + -6x + 2x2 + (12x + -15x2) = 0 Reorder the terms: 8 + -6x + 12x + 2x2 + -15x2 = 0 Combine like terms: -6x + 12x = 6x 8 + 6x + 2x2 + -15x2 = 0 Combine like terms: 2x2 + -15x2 = -13x2 8 + 6x + -13x2 = 0 Solving 8 + 6x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.6153846154 + -0.4615384615x + x2 = 0 Move the constant term to the right: Add '0.6153846154' to each side of the equation. -0.6153846154 + -0.4615384615x + 0.6153846154 + x2 = 0 + 0.6153846154 Reorder the terms: -0.6153846154 + 0.6153846154 + -0.4615384615x + x2 = 0 + 0.6153846154 Combine like terms: -0.6153846154 + 0.6153846154 = 0.0000000000 0.0000000000 + -0.4615384615x + x2 = 0 + 0.6153846154 -0.4615384615x + x2 = 0 + 0.6153846154 Combine like terms: 0 + 0.6153846154 = 0.6153846154 -0.4615384615x + x2 = 0.6153846154 The x term is -0.4615384615x. Take half its coefficient (-0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. -0.4615384615x + 0.05325443788 + x2 = 0.6153846154 + 0.05325443788 Reorder the terms: 0.05325443788 + -0.4615384615x + x2 = 0.6153846154 + 0.05325443788 Combine like terms: 0.6153846154 + 0.05325443788 = 0.66863905328 0.05325443788 + -0.4615384615x + x2 = 0.66863905328 Factor a perfect square on the left side: (x + -0.2307692308)(x + -0.2307692308) = 0.66863905328 Calculate the square root of the right side: 0.817703524 Break this problem into two subproblems by setting (x + -0.2307692308) equal to 0.817703524 and -0.817703524.Subproblem 1
x + -0.2307692308 = 0.817703524 Simplifying x + -0.2307692308 = 0.817703524 Reorder the terms: -0.2307692308 + x = 0.817703524 Solving -0.2307692308 + x = 0.817703524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + x = 0.817703524 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + x = 0.817703524 + 0.2307692308 x = 0.817703524 + 0.2307692308 Combine like terms: 0.817703524 + 0.2307692308 = 1.0484727548 x = 1.0484727548 Simplifying x = 1.0484727548Subproblem 2
x + -0.2307692308 = -0.817703524 Simplifying x + -0.2307692308 = -0.817703524 Reorder the terms: -0.2307692308 + x = -0.817703524 Solving -0.2307692308 + x = -0.817703524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2307692308' to each side of the equation. -0.2307692308 + 0.2307692308 + x = -0.817703524 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + x = -0.817703524 + 0.2307692308 x = -0.817703524 + 0.2307692308 Combine like terms: -0.817703524 + 0.2307692308 = -0.5869342932 x = -0.5869342932 Simplifying x = -0.5869342932Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0484727548, -0.5869342932}
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