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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 = 1.015625 3.515625 + 3.75x + x2 = 1.015625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 1.015625 Calculate the square root of the right side: 1.007782219 Break this problem into two subproblems by setting (x + 1.875) equal to 1.007782219 and -1.007782219.Subproblem 1
x + 1.875 = 1.007782219 Simplifying x + 1.875 = 1.007782219 Reorder the terms: 1.875 + x = 1.007782219 Solving 1.875 + x = 1.007782219 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 = 1.007782219 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 1.007782219 + -1.875 x = 1.007782219 + -1.875 Combine like terms: 1.007782219 + -1.875 = -0.867217781 x = -0.867217781 Simplifying x = -0.867217781Subproblem 2
x + 1.875 = -1.007782219 Simplifying x + 1.875 = -1.007782219 Reorder the terms: 1.875 + x = -1.007782219 Solving 1.875 + x = -1.007782219 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 = -1.007782219 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -1.007782219 + -1.875 x = -1.007782219 + -1.875 Combine like terms: -1.007782219 + -1.875 = -2.882782219 x = -2.882782219 Simplifying x = -2.882782219Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.867217781, -2.882782219}
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