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Simplifying (3x + -4 + 5x2) + (7x2 + 2x + -5) = 0 Reorder the terms: (-4 + 3x + 5x2) + (7x2 + 2x + -5) = 0 Remove parenthesis around (-4 + 3x + 5x2) -4 + 3x + 5x2 + (7x2 + 2x + -5) = 0 Reorder the terms: -4 + 3x + 5x2 + (-5 + 2x + 7x2) = 0 Remove parenthesis around (-5 + 2x + 7x2) -4 + 3x + 5x2 + -5 + 2x + 7x2 = 0 Reorder the terms: -4 + -5 + 3x + 2x + 5x2 + 7x2 = 0 Combine like terms: -4 + -5 = -9 -9 + 3x + 2x + 5x2 + 7x2 = 0 Combine like terms: 3x + 2x = 5x -9 + 5x + 5x2 + 7x2 = 0 Combine like terms: 5x2 + 7x2 = 12x2 -9 + 5x + 12x2 = 0 Solving -9 + 5x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.75 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.4166666667x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.4166666667x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.4166666667x + x2 = 0 + 0.75 0.4166666667x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.4166666667x + x2 = 0.75 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = 0.75 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = 0.75 + 0.04340277781 Combine like terms: 0.75 + 0.04340277781 = 0.79340277781 0.04340277781 + 0.4166666667x + x2 = 0.79340277781 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = 0.79340277781 Calculate the square root of the right side: 0.890731597 Break this problem into two subproblems by setting (x + 0.2083333334) equal to 0.890731597 and -0.890731597.Subproblem 1
x + 0.2083333334 = 0.890731597 Simplifying x + 0.2083333334 = 0.890731597 Reorder the terms: 0.2083333334 + x = 0.890731597 Solving 0.2083333334 + x = 0.890731597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = 0.890731597 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = 0.890731597 + -0.2083333334 x = 0.890731597 + -0.2083333334 Combine like terms: 0.890731597 + -0.2083333334 = 0.6823982636 x = 0.6823982636 Simplifying x = 0.6823982636Subproblem 2
x + 0.2083333334 = -0.890731597 Simplifying x + 0.2083333334 = -0.890731597 Reorder the terms: 0.2083333334 + x = -0.890731597 Solving 0.2083333334 + x = -0.890731597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + x = -0.890731597 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + x = -0.890731597 + -0.2083333334 x = -0.890731597 + -0.2083333334 Combine like terms: -0.890731597 + -0.2083333334 = -1.0990649304 x = -1.0990649304 Simplifying x = -1.0990649304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6823982636, -1.0990649304}
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