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Simplifying 2x2 + -9x + 3 + -4x + -17x2 = 0 Reorder the terms: 3 + -9x + -4x + 2x2 + -17x2 = 0 Combine like terms: -9x + -4x = -13x 3 + -13x + 2x2 + -17x2 = 0 Combine like terms: 2x2 + -17x2 = -15x2 3 + -13x + -15x2 = 0 Solving 3 + -13x + -15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.2 + 0.8666666667x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.8666666667x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.8666666667x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.8666666667x + x2 = 0 + 0.2 0.8666666667x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.8666666667x + x2 = 0.2 The x term is 0.8666666667x. Take half its coefficient (0.4333333334). Square it (0.1877777778) and add it to both sides. Add '0.1877777778' to each side of the equation. 0.8666666667x + 0.1877777778 + x2 = 0.2 + 0.1877777778 Reorder the terms: 0.1877777778 + 0.8666666667x + x2 = 0.2 + 0.1877777778 Combine like terms: 0.2 + 0.1877777778 = 0.3877777778 0.1877777778 + 0.8666666667x + x2 = 0.3877777778 Factor a perfect square on the left side: (x + 0.4333333334)(x + 0.4333333334) = 0.3877777778 Calculate the square root of the right side: 0.622718056 Break this problem into two subproblems by setting (x + 0.4333333334) equal to 0.622718056 and -0.622718056.Subproblem 1
x + 0.4333333334 = 0.622718056 Simplifying x + 0.4333333334 = 0.622718056 Reorder the terms: 0.4333333334 + x = 0.622718056 Solving 0.4333333334 + x = 0.622718056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4333333334' to each side of the equation. 0.4333333334 + -0.4333333334 + x = 0.622718056 + -0.4333333334 Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000 0.0000000000 + x = 0.622718056 + -0.4333333334 x = 0.622718056 + -0.4333333334 Combine like terms: 0.622718056 + -0.4333333334 = 0.1893847226 x = 0.1893847226 Simplifying x = 0.1893847226Subproblem 2
x + 0.4333333334 = -0.622718056 Simplifying x + 0.4333333334 = -0.622718056 Reorder the terms: 0.4333333334 + x = -0.622718056 Solving 0.4333333334 + x = -0.622718056 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4333333334' to each side of the equation. 0.4333333334 + -0.4333333334 + x = -0.622718056 + -0.4333333334 Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000 0.0000000000 + x = -0.622718056 + -0.4333333334 x = -0.622718056 + -0.4333333334 Combine like terms: -0.622718056 + -0.4333333334 = -1.0560513894 x = -1.0560513894 Simplifying x = -1.0560513894Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1893847226, -1.0560513894}
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