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Simplifying 3x + -6 + x2 = 24x Reorder the terms: -6 + 3x + x2 = 24x Solving -6 + 3x + x2 = 24x Solving for variable 'x'. Reorder the terms: -6 + 3x + -24x + x2 = 24x + -24x Combine like terms: 3x + -24x = -21x -6 + -21x + x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -6 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -21x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -21x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -21x + x2 = 0 + 6 -21x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -21x + x2 = 6 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 6 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 6 + 110.25 Combine like terms: 6 + 110.25 = 116.25 110.25 + -21x + x2 = 116.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + -10.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + -10.5 = 10.781929326 Simplifying x + -10.5 = 10.781929326 Reorder the terms: -10.5 + x = 10.781929326 Solving -10.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 10.781929326 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 10.781929326 + 10.5 x = 10.781929326 + 10.5 Combine like terms: 10.781929326 + 10.5 = 21.281929326 x = 21.281929326 Simplifying x = 21.281929326Subproblem 2
x + -10.5 = -10.781929326 Simplifying x + -10.5 = -10.781929326 Reorder the terms: -10.5 + x = -10.781929326 Solving -10.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -10.781929326 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -10.781929326 + 10.5 x = -10.781929326 + 10.5 Combine like terms: -10.781929326 + 10.5 = -0.281929326 x = -0.281929326 Simplifying x = -0.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.281929326, -0.281929326}
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