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Simplifying 19x2 + 30x + -153 = 0 Reorder the terms: -153 + 30x + 19x2 = 0 Solving -153 + 30x + 19x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -8.052631579 + 1.578947368x + x2 = 0 Move the constant term to the right: Add '8.052631579' to each side of the equation. -8.052631579 + 1.578947368x + 8.052631579 + x2 = 0 + 8.052631579 Reorder the terms: -8.052631579 + 8.052631579 + 1.578947368x + x2 = 0 + 8.052631579 Combine like terms: -8.052631579 + 8.052631579 = 0.000000000 0.000000000 + 1.578947368x + x2 = 0 + 8.052631579 1.578947368x + x2 = 0 + 8.052631579 Combine like terms: 0 + 8.052631579 = 8.052631579 1.578947368x + x2 = 8.052631579 The x term is 1.578947368x. Take half its coefficient (0.789473684). Square it (0.6232686977) and add it to both sides. Add '0.6232686977' to each side of the equation. 1.578947368x + 0.6232686977 + x2 = 8.052631579 + 0.6232686977 Reorder the terms: 0.6232686977 + 1.578947368x + x2 = 8.052631579 + 0.6232686977 Combine like terms: 8.052631579 + 0.6232686977 = 8.6759002767 0.6232686977 + 1.578947368x + x2 = 8.6759002767 Factor a perfect square on the left side: (x + 0.789473684)(x + 0.789473684) = 8.6759002767 Calculate the square root of the right side: 2.945488122 Break this problem into two subproblems by setting (x + 0.789473684) equal to 2.945488122 and -2.945488122.Subproblem 1
x + 0.789473684 = 2.945488122 Simplifying x + 0.789473684 = 2.945488122 Reorder the terms: 0.789473684 + x = 2.945488122 Solving 0.789473684 + x = 2.945488122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.789473684' to each side of the equation. 0.789473684 + -0.789473684 + x = 2.945488122 + -0.789473684 Combine like terms: 0.789473684 + -0.789473684 = 0.000000000 0.000000000 + x = 2.945488122 + -0.789473684 x = 2.945488122 + -0.789473684 Combine like terms: 2.945488122 + -0.789473684 = 2.156014438 x = 2.156014438 Simplifying x = 2.156014438Subproblem 2
x + 0.789473684 = -2.945488122 Simplifying x + 0.789473684 = -2.945488122 Reorder the terms: 0.789473684 + x = -2.945488122 Solving 0.789473684 + x = -2.945488122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.789473684' to each side of the equation. 0.789473684 + -0.789473684 + x = -2.945488122 + -0.789473684 Combine like terms: 0.789473684 + -0.789473684 = 0.000000000 0.000000000 + x = -2.945488122 + -0.789473684 x = -2.945488122 + -0.789473684 Combine like terms: -2.945488122 + -0.789473684 = -3.734961806 x = -3.734961806 Simplifying x = -3.734961806Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.156014438, -3.734961806}
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