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Simplifying 15x2 + 48x + 8 = 0 Reorder the terms: 8 + 48x + 15x2 = 0 Solving 8 + 48x + 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'. 0.5333333333 + 3.2x + x2 = 0 Move the constant term to the right: Add '-0.5333333333' to each side of the equation. 0.5333333333 + 3.2x + -0.5333333333 + x2 = 0 + -0.5333333333 Reorder the terms: 0.5333333333 + -0.5333333333 + 3.2x + x2 = 0 + -0.5333333333 Combine like terms: 0.5333333333 + -0.5333333333 = 0.0000000000 0.0000000000 + 3.2x + x2 = 0 + -0.5333333333 3.2x + x2 = 0 + -0.5333333333 Combine like terms: 0 + -0.5333333333 = -0.5333333333 3.2x + x2 = -0.5333333333 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = -0.5333333333 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = -0.5333333333 + 2.56 Combine like terms: -0.5333333333 + 2.56 = 2.0266666667 2.56 + 3.2x + x2 = 2.0266666667 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 2.0266666667 Calculate the square root of the right side: 1.423610434 Break this problem into two subproblems by setting (x + 1.6) equal to 1.423610434 and -1.423610434.Subproblem 1
x + 1.6 = 1.423610434 Simplifying x + 1.6 = 1.423610434 Reorder the terms: 1.6 + x = 1.423610434 Solving 1.6 + x = 1.423610434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.423610434 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.423610434 + -1.6 x = 1.423610434 + -1.6 Combine like terms: 1.423610434 + -1.6 = -0.176389566 x = -0.176389566 Simplifying x = -0.176389566Subproblem 2
x + 1.6 = -1.423610434 Simplifying x + 1.6 = -1.423610434 Reorder the terms: 1.6 + x = -1.423610434 Solving 1.6 + x = -1.423610434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.423610434 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.423610434 + -1.6 x = -1.423610434 + -1.6 Combine like terms: -1.423610434 + -1.6 = -3.023610434 x = -3.023610434 Simplifying x = -3.023610434Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.176389566, -3.023610434}
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