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Simplifying 5(4x2 + -8x + 3) + -7(6x2 + -4x + 11) = 0 Reorder the terms: 5(3 + -8x + 4x2) + -7(6x2 + -4x + 11) = 0 (3 * 5 + -8x * 5 + 4x2 * 5) + -7(6x2 + -4x + 11) = 0 (15 + -40x + 20x2) + -7(6x2 + -4x + 11) = 0 Reorder the terms: 15 + -40x + 20x2 + -7(11 + -4x + 6x2) = 0 15 + -40x + 20x2 + (11 * -7 + -4x * -7 + 6x2 * -7) = 0 15 + -40x + 20x2 + (-77 + 28x + -42x2) = 0 Reorder the terms: 15 + -77 + -40x + 28x + 20x2 + -42x2 = 0 Combine like terms: 15 + -77 = -62 -62 + -40x + 28x + 20x2 + -42x2 = 0 Combine like terms: -40x + 28x = -12x -62 + -12x + 20x2 + -42x2 = 0 Combine like terms: 20x2 + -42x2 = -22x2 -62 + -12x + -22x2 = 0 Solving -62 + -12x + -22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(31 + 6x + 11x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(31 + 6x + 11x2)' equal to zero and attempt to solve: Simplifying 31 + 6x + 11x2 = 0 Solving 31 + 6x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 2.818181818 + 0.5454545455x + x2 = 0 Move the constant term to the right: Add '-2.818181818' to each side of the equation. 2.818181818 + 0.5454545455x + -2.818181818 + x2 = 0 + -2.818181818 Reorder the terms: 2.818181818 + -2.818181818 + 0.5454545455x + x2 = 0 + -2.818181818 Combine like terms: 2.818181818 + -2.818181818 = 0.000000000 0.000000000 + 0.5454545455x + x2 = 0 + -2.818181818 0.5454545455x + x2 = 0 + -2.818181818 Combine like terms: 0 + -2.818181818 = -2.818181818 0.5454545455x + x2 = -2.818181818 The x term is 0.5454545455x. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455x + 0.07438016533 + x2 = -2.818181818 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455x + x2 = -2.818181818 + 0.07438016533 Combine like terms: -2.818181818 + 0.07438016533 = -2.74380165267 0.07438016533 + 0.5454545455x + x2 = -2.74380165267 Factor a perfect square on the left side: (x + 0.2727272728)(x + 0.2727272728) = -2.74380165267 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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