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Simplifying 4x2 + -3.5x = 26 Reorder the terms: -3.5x + 4x2 = 26 Solving -3.5x + 4x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + -3.5x + 4x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + -3.5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.5 + -0.875x + x2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -0.875x + 6.5 + x2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -0.875x + x2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -0.875x + x2 = 0 + 6.5 -0.875x + x2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -0.875x + x2 = 6.5 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 6.5 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 6.5 + 0.19140625 Combine like terms: 6.5 + 0.19140625 = 6.69140625 0.19140625 + -0.875x + x2 = 6.69140625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 6.69140625 Calculate the square root of the right side: 2.586775261 Break this problem into two subproblems by setting (x + -0.4375) equal to 2.586775261 and -2.586775261.Subproblem 1
x + -0.4375 = 2.586775261 Simplifying x + -0.4375 = 2.586775261 Reorder the terms: -0.4375 + x = 2.586775261 Solving -0.4375 + x = 2.586775261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 2.586775261 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 2.586775261 + 0.4375 x = 2.586775261 + 0.4375 Combine like terms: 2.586775261 + 0.4375 = 3.024275261 x = 3.024275261 Simplifying x = 3.024275261Subproblem 2
x + -0.4375 = -2.586775261 Simplifying x + -0.4375 = -2.586775261 Reorder the terms: -0.4375 + x = -2.586775261 Solving -0.4375 + x = -2.586775261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -2.586775261 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -2.586775261 + 0.4375 x = -2.586775261 + 0.4375 Combine like terms: -2.586775261 + 0.4375 = -2.149275261 x = -2.149275261 Simplifying x = -2.149275261Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.024275261, -2.149275261}
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