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Simplifying 4x2 + -15x + -10 = 0 Reorder the terms: -10 + -15x + 4x2 = 0 Solving -10 + -15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.5 + -3.75x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -3.75x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -3.75x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -3.75x + x2 = 0 + 2.5 -3.75x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -3.75x + x2 = 2.5 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 2.5 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 2.5 + 3.515625 Combine like terms: 2.5 + 3.515625 = 6.015625 3.515625 + -3.75x + x2 = 6.015625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (x + -1.875) equal to 2.452677109 and -2.452677109.Subproblem 1
x + -1.875 = 2.452677109 Simplifying x + -1.875 = 2.452677109 Reorder the terms: -1.875 + x = 2.452677109 Solving -1.875 + x = 2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 2.452677109 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.452677109 + 1.875 x = 2.452677109 + 1.875 Combine like terms: 2.452677109 + 1.875 = 4.327677109 x = 4.327677109 Simplifying x = 4.327677109Subproblem 2
x + -1.875 = -2.452677109 Simplifying x + -1.875 = -2.452677109 Reorder the terms: -1.875 + x = -2.452677109 Solving -1.875 + x = -2.452677109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -2.452677109 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.452677109 + 1.875 x = -2.452677109 + 1.875 Combine like terms: -2.452677109 + 1.875 = -0.577677109 x = -0.577677109 Simplifying x = -0.577677109Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.327677109, -0.577677109}
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