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Simplifying 5(3x + -4) + -1(x2 + 2) + -2x(x + -3) = 0 Reorder the terms: 5(-4 + 3x) + -1(x2 + 2) + -2x(x + -3) = 0 (-4 * 5 + 3x * 5) + -1(x2 + 2) + -2x(x + -3) = 0 (-20 + 15x) + -1(x2 + 2) + -2x(x + -3) = 0 Reorder the terms: -20 + 15x + -1(2 + x2) + -2x(x + -3) = 0 -20 + 15x + (2 * -1 + x2 * -1) + -2x(x + -3) = 0 -20 + 15x + (-2 + -1x2) + -2x(x + -3) = 0 Reorder the terms: -20 + 15x + -2 + -1x2 + -2x(-3 + x) = 0 -20 + 15x + -2 + -1x2 + (-3 * -2x + x * -2x) = 0 -20 + 15x + -2 + -1x2 + (6x + -2x2) = 0 Reorder the terms: -20 + -2 + 15x + 6x + -1x2 + -2x2 = 0 Combine like terms: -20 + -2 = -22 -22 + 15x + 6x + -1x2 + -2x2 = 0 Combine like terms: 15x + 6x = 21x -22 + 21x + -1x2 + -2x2 = 0 Combine like terms: -1x2 + -2x2 = -3x2 -22 + 21x + -3x2 = 0 Solving -22 + 21x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 7.333333333 + -7x + x2 = 0 Move the constant term to the right: Add '-7.333333333' to each side of the equation. 7.333333333 + -7x + -7.333333333 + x2 = 0 + -7.333333333 Reorder the terms: 7.333333333 + -7.333333333 + -7x + x2 = 0 + -7.333333333 Combine like terms: 7.333333333 + -7.333333333 = 0.000000000 0.000000000 + -7x + x2 = 0 + -7.333333333 -7x + x2 = 0 + -7.333333333 Combine like terms: 0 + -7.333333333 = -7.333333333 -7x + x2 = -7.333333333 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -7.333333333 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -7.333333333 + 12.25 Combine like terms: -7.333333333 + 12.25 = 4.916666667 12.25 + -7x + x2 = 4.916666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 4.916666667 Calculate the square root of the right side: 2.217355783 Break this problem into two subproblems by setting (x + -3.5) equal to 2.217355783 and -2.217355783.Subproblem 1
x + -3.5 = 2.217355783 Simplifying x + -3.5 = 2.217355783 Reorder the terms: -3.5 + x = 2.217355783 Solving -3.5 + x = 2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.217355783 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.217355783 + 3.5 x = 2.217355783 + 3.5 Combine like terms: 2.217355783 + 3.5 = 5.717355783 x = 5.717355783 Simplifying x = 5.717355783Subproblem 2
x + -3.5 = -2.217355783 Simplifying x + -3.5 = -2.217355783 Reorder the terms: -3.5 + x = -2.217355783 Solving -3.5 + x = -2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.217355783 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.217355783 + 3.5 x = -2.217355783 + 3.5 Combine like terms: -2.217355783 + 3.5 = 1.282644217 x = 1.282644217 Simplifying x = 1.282644217Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.717355783, 1.282644217}
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