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Simplifying 4x2 + 10x + -143 = 0 Reorder the terms: -143 + 10x + 4x2 = 0 Solving -143 + 10x + 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'. -35.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '35.75' to each side of the equation. -35.75 + 2.5x + 35.75 + x2 = 0 + 35.75 Reorder the terms: -35.75 + 35.75 + 2.5x + x2 = 0 + 35.75 Combine like terms: -35.75 + 35.75 = 0.00 0.00 + 2.5x + x2 = 0 + 35.75 2.5x + x2 = 0 + 35.75 Combine like terms: 0 + 35.75 = 35.75 2.5x + x2 = 35.75 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 35.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 35.75 + 1.5625 Combine like terms: 35.75 + 1.5625 = 37.3125 1.5625 + 2.5x + x2 = 37.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 37.3125 Calculate the square root of the right side: 6.108395861 Break this problem into two subproblems by setting (x + 1.25) equal to 6.108395861 and -6.108395861.Subproblem 1
x + 1.25 = 6.108395861 Simplifying x + 1.25 = 6.108395861 Reorder the terms: 1.25 + x = 6.108395861 Solving 1.25 + x = 6.108395861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 6.108395861 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 6.108395861 + -1.25 x = 6.108395861 + -1.25 Combine like terms: 6.108395861 + -1.25 = 4.858395861 x = 4.858395861 Simplifying x = 4.858395861Subproblem 2
x + 1.25 = -6.108395861 Simplifying x + 1.25 = -6.108395861 Reorder the terms: 1.25 + x = -6.108395861 Solving 1.25 + x = -6.108395861 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -6.108395861 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -6.108395861 + -1.25 x = -6.108395861 + -1.25 Combine like terms: -6.108395861 + -1.25 = -7.358395861 x = -7.358395861 Simplifying x = -7.358395861Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.858395861, -7.358395861}
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