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Simplifying 15x2 + -11x + -3 = 0 Reorder the terms: -3 + -11x + 15x2 = 0 Solving -3 + -11x + 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'. -0.2 + -0.7333333333x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.7333333333x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.7333333333x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.7333333333x + x2 = 0 + 0.2 -0.7333333333x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.7333333333x + x2 = 0.2 The x term is -0.7333333333x. Take half its coefficient (-0.3666666667). Square it (0.1344444445) and add it to both sides. Add '0.1344444445' to each side of the equation. -0.7333333333x + 0.1344444445 + x2 = 0.2 + 0.1344444445 Reorder the terms: 0.1344444445 + -0.7333333333x + x2 = 0.2 + 0.1344444445 Combine like terms: 0.2 + 0.1344444445 = 0.3344444445 0.1344444445 + -0.7333333333x + x2 = 0.3344444445 Factor a perfect square on the left side: (x + -0.3666666667)(x + -0.3666666667) = 0.3344444445 Calculate the square root of the right side: 0.578311719 Break this problem into two subproblems by setting (x + -0.3666666667) equal to 0.578311719 and -0.578311719.Subproblem 1
x + -0.3666666667 = 0.578311719 Simplifying x + -0.3666666667 = 0.578311719 Reorder the terms: -0.3666666667 + x = 0.578311719 Solving -0.3666666667 + x = 0.578311719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3666666667' to each side of the equation. -0.3666666667 + 0.3666666667 + x = 0.578311719 + 0.3666666667 Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000 0.0000000000 + x = 0.578311719 + 0.3666666667 x = 0.578311719 + 0.3666666667 Combine like terms: 0.578311719 + 0.3666666667 = 0.9449783857 x = 0.9449783857 Simplifying x = 0.9449783857Subproblem 2
x + -0.3666666667 = -0.578311719 Simplifying x + -0.3666666667 = -0.578311719 Reorder the terms: -0.3666666667 + x = -0.578311719 Solving -0.3666666667 + x = -0.578311719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3666666667' to each side of the equation. -0.3666666667 + 0.3666666667 + x = -0.578311719 + 0.3666666667 Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000 0.0000000000 + x = -0.578311719 + 0.3666666667 x = -0.578311719 + 0.3666666667 Combine like terms: -0.578311719 + 0.3666666667 = -0.2116450523 x = -0.2116450523 Simplifying x = -0.2116450523Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9449783857, -0.2116450523}
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