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Simplifying 6x2 + 19x = -7 Reorder the terms: 19x + 6x2 = -7 Solving 19x + 6x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 19x + 6x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 3.166666667x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 3.166666667x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 3.166666667x + x2 = 0 + -1.166666667 3.166666667x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 3.166666667x + x2 = -1.166666667 The x term is 3.166666667x. Take half its coefficient (1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. 3.166666667x + 2.506944447 + x2 = -1.166666667 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = -1.166666667 + 2.506944447 Combine like terms: -1.166666667 + 2.506944447 = 1.34027778 2.506944447 + 3.166666667x + x2 = 1.34027778 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 1.34027778 Calculate the square root of the right side: 1.157703667 Break this problem into two subproblems by setting (x + 1.583333334) equal to 1.157703667 and -1.157703667.Subproblem 1
x + 1.583333334 = 1.157703667 Simplifying x + 1.583333334 = 1.157703667 Reorder the terms: 1.583333334 + x = 1.157703667 Solving 1.583333334 + x = 1.157703667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + x = 1.157703667 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 1.157703667 + -1.583333334 x = 1.157703667 + -1.583333334 Combine like terms: 1.157703667 + -1.583333334 = -0.425629667 x = -0.425629667 Simplifying x = -0.425629667Subproblem 2
x + 1.583333334 = -1.157703667 Simplifying x + 1.583333334 = -1.157703667 Reorder the terms: 1.583333334 + x = -1.157703667 Solving 1.583333334 + x = -1.157703667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + x = -1.157703667 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -1.157703667 + -1.583333334 x = -1.157703667 + -1.583333334 Combine like terms: -1.157703667 + -1.583333334 = -2.741037001 x = -2.741037001 Simplifying x = -2.741037001Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.425629667, -2.741037001}
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