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Simplifying 15x2 + -4x + 0.24 = 0 Reorder the terms: 0.24 + -4x + 15x2 = 0 Solving 0.24 + -4x + 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'. 0.016 + -0.2666666667x + x2 = 0 Move the constant term to the right: Add '-0.016' to each side of the equation. 0.016 + -0.2666666667x + -0.016 + x2 = 0 + -0.016 Reorder the terms: 0.016 + -0.016 + -0.2666666667x + x2 = 0 + -0.016 Combine like terms: 0.016 + -0.016 = 0.000 0.000 + -0.2666666667x + x2 = 0 + -0.016 -0.2666666667x + x2 = 0 + -0.016 Combine like terms: 0 + -0.016 = -0.016 -0.2666666667x + x2 = -0.016 The x term is -0.2666666667x. Take half its coefficient (-0.1333333334). Square it (0.01777777780) and add it to both sides. Add '0.01777777780' to each side of the equation. -0.2666666667x + 0.01777777780 + x2 = -0.016 + 0.01777777780 Reorder the terms: 0.01777777780 + -0.2666666667x + x2 = -0.016 + 0.01777777780 Combine like terms: -0.016 + 0.01777777780 = 0.0017777778 0.01777777780 + -0.2666666667x + x2 = 0.0017777778 Factor a perfect square on the left side: (x + -0.1333333334)(x + -0.1333333334) = 0.0017777778 Calculate the square root of the right side: 0.042163702 Break this problem into two subproblems by setting (x + -0.1333333334) equal to 0.042163702 and -0.042163702.Subproblem 1
x + -0.1333333334 = 0.042163702 Simplifying x + -0.1333333334 = 0.042163702 Reorder the terms: -0.1333333334 + x = 0.042163702 Solving -0.1333333334 + x = 0.042163702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = 0.042163702 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = 0.042163702 + 0.1333333334 x = 0.042163702 + 0.1333333334 Combine like terms: 0.042163702 + 0.1333333334 = 0.1754970354 x = 0.1754970354 Simplifying x = 0.1754970354Subproblem 2
x + -0.1333333334 = -0.042163702 Simplifying x + -0.1333333334 = -0.042163702 Reorder the terms: -0.1333333334 + x = -0.042163702 Solving -0.1333333334 + x = -0.042163702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1333333334' to each side of the equation. -0.1333333334 + 0.1333333334 + x = -0.042163702 + 0.1333333334 Combine like terms: -0.1333333334 + 0.1333333334 = 0.0000000000 0.0000000000 + x = -0.042163702 + 0.1333333334 x = -0.042163702 + 0.1333333334 Combine like terms: -0.042163702 + 0.1333333334 = 0.0911696314 x = 0.0911696314 Simplifying x = 0.0911696314Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1754970354, 0.0911696314}
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