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Simplifying 10x2 + -15x + 2 = 0 Reorder the terms: 2 + -15x + 10x2 = 0 Solving 2 + -15x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.2 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.5x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.5x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.5x + x2 = 0 + -0.2 -1.5x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.5x + x2 = -0.2 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -0.2 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.2 + 0.5625 Combine like terms: -0.2 + 0.5625 = 0.3625 0.5625 + -1.5x + x2 = 0.3625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.3625 Calculate the square root of the right side: 0.602079729 Break this problem into two subproblems by setting (x + -0.75) equal to 0.602079729 and -0.602079729.Subproblem 1
x + -0.75 = 0.602079729 Simplifying x + -0.75 = 0.602079729 Reorder the terms: -0.75 + x = 0.602079729 Solving -0.75 + x = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.602079729 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.602079729 + 0.75 x = 0.602079729 + 0.75 Combine like terms: 0.602079729 + 0.75 = 1.352079729 x = 1.352079729 Simplifying x = 1.352079729Subproblem 2
x + -0.75 = -0.602079729 Simplifying x + -0.75 = -0.602079729 Reorder the terms: -0.75 + x = -0.602079729 Solving -0.75 + x = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.602079729 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.602079729 + 0.75 x = -0.602079729 + 0.75 Combine like terms: -0.602079729 + 0.75 = 0.147920271 x = 0.147920271 Simplifying x = 0.147920271Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.352079729, 0.147920271}
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