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Simplifying 4x2 + -1x = 15 Reorder the terms: -1x + 4x2 = 15 Solving -1x + 4x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + -1x + 4x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.25x + x2 = 0 + 3.75 -0.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.25x + x2 = 3.75 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 3.75 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 3.75 + 0.015625 Combine like terms: 3.75 + 0.015625 = 3.765625 0.015625 + -0.25x + x2 = 3.765625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + -0.125) equal to 1.940521837 and -1.940521837.Subproblem 1
x + -0.125 = 1.940521837 Simplifying x + -0.125 = 1.940521837 Reorder the terms: -0.125 + x = 1.940521837 Solving -0.125 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 1.940521837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.940521837 + 0.125 x = 1.940521837 + 0.125 Combine like terms: 1.940521837 + 0.125 = 2.065521837 x = 2.065521837 Simplifying x = 2.065521837Subproblem 2
x + -0.125 = -1.940521837 Simplifying x + -0.125 = -1.940521837 Reorder the terms: -0.125 + x = -1.940521837 Solving -0.125 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -1.940521837 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.940521837 + 0.125 x = -1.940521837 + 0.125 Combine like terms: -1.940521837 + 0.125 = -1.815521837 x = -1.815521837 Simplifying x = -1.815521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.065521837, -1.815521837}
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