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Simplifying 15x + 10 = 4x2 + -12x + 9 Reorder the terms: 10 + 15x = 4x2 + -12x + 9 Reorder the terms: 10 + 15x = 9 + -12x + 4x2 Solving 10 + 15x = 9 + -12x + 4x2 Solving for variable 'x'. Reorder the terms: 10 + -9 + 15x + 12x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2 Combine like terms: 10 + -9 = 1 1 + 15x + 12x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2 Combine like terms: 15x + 12x = 27x 1 + 27x + -4x2 = 9 + -12x + 4x2 + -9 + 12x + -4x2 Reorder the terms: 1 + 27x + -4x2 = 9 + -9 + -12x + 12x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 1 + 27x + -4x2 = 0 + -12x + 12x + 4x2 + -4x2 1 + 27x + -4x2 = -12x + 12x + 4x2 + -4x2 Combine like terms: -12x + 12x = 0 1 + 27x + -4x2 = 0 + 4x2 + -4x2 1 + 27x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 1 + 27x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -6.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -6.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -6.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -6.75x + x2 = 0 + 0.25 -6.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -6.75x + x2 = 0.25 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = 0.25 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 0.25 + 11.390625 Combine like terms: 0.25 + 11.390625 = 11.640625 11.390625 + -6.75x + x2 = 11.640625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 11.640625 Calculate the square root of the right side: 3.411836016 Break this problem into two subproblems by setting (x + -3.375) equal to 3.411836016 and -3.411836016.Subproblem 1
x + -3.375 = 3.411836016 Simplifying x + -3.375 = 3.411836016 Reorder the terms: -3.375 + x = 3.411836016 Solving -3.375 + x = 3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 3.411836016 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 3.411836016 + 3.375 x = 3.411836016 + 3.375 Combine like terms: 3.411836016 + 3.375 = 6.786836016 x = 6.786836016 Simplifying x = 6.786836016Subproblem 2
x + -3.375 = -3.411836016 Simplifying x + -3.375 = -3.411836016 Reorder the terms: -3.375 + x = -3.411836016 Solving -3.375 + x = -3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -3.411836016 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -3.411836016 + 3.375 x = -3.411836016 + 3.375 Combine like terms: -3.411836016 + 3.375 = -0.036836016 x = -0.036836016 Simplifying x = -0.036836016Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.786836016, -0.036836016}
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