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Simplifying 0 = 3x2 + -24x + -5 Reorder the terms: 0 = -5 + -24x + 3x2 Solving 0 = -5 + -24x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 5 = 5 5 + 24x + -3x2 = -5 + -24x + 3x2 + 5 + 24x + -3x2 Reorder the terms: 5 + 24x + -3x2 = -5 + 5 + -24x + 24x + 3x2 + -3x2 Combine like terms: -5 + 5 = 0 5 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2 5 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2 Combine like terms: -24x + 24x = 0 5 + 24x + -3x2 = 0 + 3x2 + -3x2 5 + 24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 5 + 24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -8x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -8x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -8x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + 1.666666667 -8x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -8x + x2 = 1.666666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 1.666666667 + 16 Reorder the terms: 16 + -8x + x2 = 1.666666667 + 16 Combine like terms: 1.666666667 + 16 = 17.666666667 16 + -8x + x2 = 17.666666667 Factor a perfect square on the left side: (x + -4)(x + -4) = 17.666666667 Calculate the square root of the right side: 4.203173404 Break this problem into two subproblems by setting (x + -4) equal to 4.203173404 and -4.203173404.Subproblem 1
x + -4 = 4.203173404 Simplifying x + -4 = 4.203173404 Reorder the terms: -4 + x = 4.203173404 Solving -4 + x = 4.203173404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.203173404 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.203173404 + 4 x = 4.203173404 + 4 Combine like terms: 4.203173404 + 4 = 8.203173404 x = 8.203173404 Simplifying x = 8.203173404Subproblem 2
x + -4 = -4.203173404 Simplifying x + -4 = -4.203173404 Reorder the terms: -4 + x = -4.203173404 Solving -4 + x = -4.203173404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.203173404 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.203173404 + 4 x = -4.203173404 + 4 Combine like terms: -4.203173404 + 4 = -0.203173404 x = -0.203173404 Simplifying x = -0.203173404Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.203173404, -0.203173404}
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