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Simplifying 3.2x2 + 4.5x + -7.8 = 0 Reorder the terms: -7.8 + 4.5x + 3.2x2 = 0 Solving -7.8 + 4.5x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. -2.4375 + 1.40625x + x2 = 0 Move the constant term to the right: Add '2.4375' to each side of the equation. -2.4375 + 1.40625x + 2.4375 + x2 = 0 + 2.4375 Reorder the terms: -2.4375 + 2.4375 + 1.40625x + x2 = 0 + 2.4375 Combine like terms: -2.4375 + 2.4375 = 0.0000 0.0000 + 1.40625x + x2 = 0 + 2.4375 1.40625x + x2 = 0 + 2.4375 Combine like terms: 0 + 2.4375 = 2.4375 1.40625x + x2 = 2.4375 The x term is 1.40625x. Take half its coefficient (0.703125). Square it (0.4943847656) and add it to both sides. Add '0.4943847656' to each side of the equation. 1.40625x + 0.4943847656 + x2 = 2.4375 + 0.4943847656 Reorder the terms: 0.4943847656 + 1.40625x + x2 = 2.4375 + 0.4943847656 Combine like terms: 2.4375 + 0.4943847656 = 2.9318847656 0.4943847656 + 1.40625x + x2 = 2.9318847656 Factor a perfect square on the left side: (x + 0.703125)(x + 0.703125) = 2.9318847656 Calculate the square root of the right side: 1.712274734 Break this problem into two subproblems by setting (x + 0.703125) equal to 1.712274734 and -1.712274734.Subproblem 1
x + 0.703125 = 1.712274734 Simplifying x + 0.703125 = 1.712274734 Reorder the terms: 0.703125 + x = 1.712274734 Solving 0.703125 + x = 1.712274734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.703125' to each side of the equation. 0.703125 + -0.703125 + x = 1.712274734 + -0.703125 Combine like terms: 0.703125 + -0.703125 = 0.000000 0.000000 + x = 1.712274734 + -0.703125 x = 1.712274734 + -0.703125 Combine like terms: 1.712274734 + -0.703125 = 1.009149734 x = 1.009149734 Simplifying x = 1.009149734Subproblem 2
x + 0.703125 = -1.712274734 Simplifying x + 0.703125 = -1.712274734 Reorder the terms: 0.703125 + x = -1.712274734 Solving 0.703125 + x = -1.712274734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.703125' to each side of the equation. 0.703125 + -0.703125 + x = -1.712274734 + -0.703125 Combine like terms: 0.703125 + -0.703125 = 0.000000 0.000000 + x = -1.712274734 + -0.703125 x = -1.712274734 + -0.703125 Combine like terms: -1.712274734 + -0.703125 = -2.415399734 x = -2.415399734 Simplifying x = -2.415399734Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.009149734, -2.415399734}
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