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Simplifying 4x + 15x2 + -15 = 0 Reorder the terms: -15 + 4x + 15x2 = 0 Solving -15 + 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'. -1 + 0.2666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.2666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.2666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.2666666667x + x2 = 0 + 1 0.2666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.2666666667x + x2 = 1 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 = 1 + 0.01777777780 Reorder the terms: 0.01777777780 + 0.2666666667x + x2 = 1 + 0.01777777780 Combine like terms: 1 + 0.01777777780 = 1.0177777778 0.01777777780 + 0.2666666667x + x2 = 1.0177777778 Factor a perfect square on the left side: (x + 0.1333333334)(x + 0.1333333334) = 1.0177777778 Calculate the square root of the right side: 1.00884973 Break this problem into two subproblems by setting (x + 0.1333333334) equal to 1.00884973 and -1.00884973.Subproblem 1
x + 0.1333333334 = 1.00884973 Simplifying x + 0.1333333334 = 1.00884973 Reorder the terms: 0.1333333334 + x = 1.00884973 Solving 0.1333333334 + x = 1.00884973 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 = 1.00884973 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = 1.00884973 + -0.1333333334 x = 1.00884973 + -0.1333333334 Combine like terms: 1.00884973 + -0.1333333334 = 0.8755163966 x = 0.8755163966 Simplifying x = 0.8755163966Subproblem 2
x + 0.1333333334 = -1.00884973 Simplifying x + 0.1333333334 = -1.00884973 Reorder the terms: 0.1333333334 + x = -1.00884973 Solving 0.1333333334 + x = -1.00884973 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 = -1.00884973 + -0.1333333334 Combine like terms: 0.1333333334 + -0.1333333334 = 0.0000000000 0.0000000000 + x = -1.00884973 + -0.1333333334 x = -1.00884973 + -0.1333333334 Combine like terms: -1.00884973 + -0.1333333334 = -1.1421830634 x = -1.1421830634 Simplifying x = -1.1421830634Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8755163966, -1.1421830634}
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