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Simplifying 43x2 + 62x = 25 Reorder the terms: 62x + 43x2 = 25 Solving 62x + 43x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 62x + 43x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 62x + 43x2 = 0 Begin completing the square. Divide all terms by 43 the coefficient of the squared term: Divide each side by '43'. -0.5813953488 + 1.441860465x + x2 = 0 Move the constant term to the right: Add '0.5813953488' to each side of the equation. -0.5813953488 + 1.441860465x + 0.5813953488 + x2 = 0 + 0.5813953488 Reorder the terms: -0.5813953488 + 0.5813953488 + 1.441860465x + x2 = 0 + 0.5813953488 Combine like terms: -0.5813953488 + 0.5813953488 = 0.0000000000 0.0000000000 + 1.441860465x + x2 = 0 + 0.5813953488 1.441860465x + x2 = 0 + 0.5813953488 Combine like terms: 0 + 0.5813953488 = 0.5813953488 1.441860465x + x2 = 0.5813953488 The x term is 1.441860465x. Take half its coefficient (0.7209302325). Square it (0.5197404001) and add it to both sides. Add '0.5197404001' to each side of the equation. 1.441860465x + 0.5197404001 + x2 = 0.5813953488 + 0.5197404001 Reorder the terms: 0.5197404001 + 1.441860465x + x2 = 0.5813953488 + 0.5197404001 Combine like terms: 0.5813953488 + 0.5197404001 = 1.1011357489 0.5197404001 + 1.441860465x + x2 = 1.1011357489 Factor a perfect square on the left side: (x + 0.7209302325)(x + 0.7209302325) = 1.1011357489 Calculate the square root of the right side: 1.049350156 Break this problem into two subproblems by setting (x + 0.7209302325) equal to 1.049350156 and -1.049350156.Subproblem 1
x + 0.7209302325 = 1.049350156 Simplifying x + 0.7209302325 = 1.049350156 Reorder the terms: 0.7209302325 + x = 1.049350156 Solving 0.7209302325 + x = 1.049350156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7209302325' to each side of the equation. 0.7209302325 + -0.7209302325 + x = 1.049350156 + -0.7209302325 Combine like terms: 0.7209302325 + -0.7209302325 = 0.0000000000 0.0000000000 + x = 1.049350156 + -0.7209302325 x = 1.049350156 + -0.7209302325 Combine like terms: 1.049350156 + -0.7209302325 = 0.3284199235 x = 0.3284199235 Simplifying x = 0.3284199235Subproblem 2
x + 0.7209302325 = -1.049350156 Simplifying x + 0.7209302325 = -1.049350156 Reorder the terms: 0.7209302325 + x = -1.049350156 Solving 0.7209302325 + x = -1.049350156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7209302325' to each side of the equation. 0.7209302325 + -0.7209302325 + x = -1.049350156 + -0.7209302325 Combine like terms: 0.7209302325 + -0.7209302325 = 0.0000000000 0.0000000000 + x = -1.049350156 + -0.7209302325 x = -1.049350156 + -0.7209302325 Combine like terms: -1.049350156 + -0.7209302325 = -1.7702803885 x = -1.7702803885 Simplifying x = -1.7702803885Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3284199235, -1.7702803885}
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