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Simplifying 15x2 + -24x + 4 = 0 Reorder the terms: 4 + -24x + 15x2 = 0 Solving 4 + -24x + 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'. 0.2666666667 + -1.6x + x2 = 0 Move the constant term to the right: Add '-0.2666666667' to each side of the equation. 0.2666666667 + -1.6x + -0.2666666667 + x2 = 0 + -0.2666666667 Reorder the terms: 0.2666666667 + -0.2666666667 + -1.6x + x2 = 0 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + -1.6x + x2 = 0 + -0.2666666667 -1.6x + x2 = 0 + -0.2666666667 Combine like terms: 0 + -0.2666666667 = -0.2666666667 -1.6x + x2 = -0.2666666667 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.2666666667 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.2666666667 + 0.64 Combine like terms: -0.2666666667 + 0.64 = 0.3733333333 0.64 + -1.6x + x2 = 0.3733333333 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.3733333333 Calculate the square root of the right side: 0.611010093 Break this problem into two subproblems by setting (x + -0.8) equal to 0.611010093 and -0.611010093.Subproblem 1
x + -0.8 = 0.611010093 Simplifying x + -0.8 = 0.611010093 Reorder the terms: -0.8 + x = 0.611010093 Solving -0.8 + x = 0.611010093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.611010093 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.611010093 + 0.8 x = 0.611010093 + 0.8 Combine like terms: 0.611010093 + 0.8 = 1.411010093 x = 1.411010093 Simplifying x = 1.411010093Subproblem 2
x + -0.8 = -0.611010093 Simplifying x + -0.8 = -0.611010093 Reorder the terms: -0.8 + x = -0.611010093 Solving -0.8 + x = -0.611010093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -0.611010093 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -0.611010093 + 0.8 x = -0.611010093 + 0.8 Combine like terms: -0.611010093 + 0.8 = 0.188989907 x = 0.188989907 Simplifying x = 0.188989907Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.411010093, 0.188989907}
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