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Simplifying (3x2 + -4x + 28) + (9x2 + x + -30) + -1(4x2 + -6x + 20) = 0 Reorder the terms: (28 + -4x + 3x2) + (9x2 + x + -30) + -1(4x2 + -6x + 20) = 0 Remove parenthesis around (28 + -4x + 3x2) 28 + -4x + 3x2 + (9x2 + x + -30) + -1(4x2 + -6x + 20) = 0 Reorder the terms: 28 + -4x + 3x2 + (-30 + x + 9x2) + -1(4x2 + -6x + 20) = 0 Remove parenthesis around (-30 + x + 9x2) 28 + -4x + 3x2 + -30 + x + 9x2 + -1(4x2 + -6x + 20) = 0 Reorder the terms: 28 + -4x + 3x2 + -30 + x + 9x2 + -1(20 + -6x + 4x2) = 0 28 + -4x + 3x2 + -30 + x + 9x2 + (20 * -1 + -6x * -1 + 4x2 * -1) = 0 28 + -4x + 3x2 + -30 + x + 9x2 + (-20 + 6x + -4x2) = 0 Reorder the terms: 28 + -30 + -20 + -4x + x + 6x + 3x2 + 9x2 + -4x2 = 0 Combine like terms: 28 + -30 = -2 -2 + -20 + -4x + x + 6x + 3x2 + 9x2 + -4x2 = 0 Combine like terms: -2 + -20 = -22 -22 + -4x + x + 6x + 3x2 + 9x2 + -4x2 = 0 Combine like terms: -4x + x = -3x -22 + -3x + 6x + 3x2 + 9x2 + -4x2 = 0 Combine like terms: -3x + 6x = 3x -22 + 3x + 3x2 + 9x2 + -4x2 = 0 Combine like terms: 3x2 + 9x2 = 12x2 -22 + 3x + 12x2 + -4x2 = 0 Combine like terms: 12x2 + -4x2 = 8x2 -22 + 3x + 8x2 = 0 Solving -22 + 3x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.75 + 0.375x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 0.375x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 0.375x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 0.375x + x2 = 0 + 2.75 0.375x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 0.375x + x2 = 2.75 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 2.75 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 2.75 + 0.03515625 Combine like terms: 2.75 + 0.03515625 = 2.78515625 0.03515625 + 0.375x + x2 = 2.78515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 2.78515625 Calculate the square root of the right side: 1.66887874 Break this problem into two subproblems by setting (x + 0.1875) equal to 1.66887874 and -1.66887874.Subproblem 1
x + 0.1875 = 1.66887874 Simplifying x + 0.1875 = 1.66887874 Reorder the terms: 0.1875 + x = 1.66887874 Solving 0.1875 + x = 1.66887874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 1.66887874 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.66887874 + -0.1875 x = 1.66887874 + -0.1875 Combine like terms: 1.66887874 + -0.1875 = 1.48137874 x = 1.48137874 Simplifying x = 1.48137874Subproblem 2
x + 0.1875 = -1.66887874 Simplifying x + 0.1875 = -1.66887874 Reorder the terms: 0.1875 + x = -1.66887874 Solving 0.1875 + x = -1.66887874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -1.66887874 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.66887874 + -0.1875 x = -1.66887874 + -0.1875 Combine like terms: -1.66887874 + -0.1875 = -1.85637874 x = -1.85637874 Simplifying x = -1.85637874Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.48137874, -1.85637874}
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