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Simplifying 4x2 + 10x + -3 = 0 Reorder the terms: -3 + 10x + 4x2 = 0 Solving -3 + 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'. -0.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 2.5x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 2.5x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 2.5x + x2 = 0 + 0.75 2.5x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 2.5x + x2 = 0.75 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 = 0.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.75 + 1.5625 Combine like terms: 0.75 + 1.5625 = 2.3125 1.5625 + 2.5x + x2 = 2.3125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.3125 Calculate the square root of the right side: 1.520690633 Break this problem into two subproblems by setting (x + 1.25) equal to 1.520690633 and -1.520690633.Subproblem 1
x + 1.25 = 1.520690633 Simplifying x + 1.25 = 1.520690633 Reorder the terms: 1.25 + x = 1.520690633 Solving 1.25 + x = 1.520690633 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 = 1.520690633 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.520690633 + -1.25 x = 1.520690633 + -1.25 Combine like terms: 1.520690633 + -1.25 = 0.270690633 x = 0.270690633 Simplifying x = 0.270690633Subproblem 2
x + 1.25 = -1.520690633 Simplifying x + 1.25 = -1.520690633 Reorder the terms: 1.25 + x = -1.520690633 Solving 1.25 + x = -1.520690633 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 = -1.520690633 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.520690633 + -1.25 x = -1.520690633 + -1.25 Combine like terms: -1.520690633 + -1.25 = -2.770690633 x = -2.770690633 Simplifying x = -2.770690633Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.270690633, -2.770690633}
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