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Simplifying 430 = 0.1x2 + 2.4x + 25 Reorder the terms: 430 = 25 + 2.4x + 0.1x2 Solving 430 = 25 + 2.4x + 0.1x2 Solving for variable 'x'. Combine like terms: 430 + -25 = 405 405 + -2.4x + -0.1x2 = 25 + 2.4x + 0.1x2 + -25 + -2.4x + -0.1x2 Reorder the terms: 405 + -2.4x + -0.1x2 = 25 + -25 + 2.4x + -2.4x + 0.1x2 + -0.1x2 Combine like terms: 25 + -25 = 0 405 + -2.4x + -0.1x2 = 0 + 2.4x + -2.4x + 0.1x2 + -0.1x2 405 + -2.4x + -0.1x2 = 2.4x + -2.4x + 0.1x2 + -0.1x2 Combine like terms: 2.4x + -2.4x = 0.0 405 + -2.4x + -0.1x2 = 0.0 + 0.1x2 + -0.1x2 405 + -2.4x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 405 + -2.4x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -4050 + 24x + x2 = 0 Move the constant term to the right: Add '4050' to each side of the equation. -4050 + 24x + 4050 + x2 = 0 + 4050 Reorder the terms: -4050 + 4050 + 24x + x2 = 0 + 4050 Combine like terms: -4050 + 4050 = 0 0 + 24x + x2 = 0 + 4050 24x + x2 = 0 + 4050 Combine like terms: 0 + 4050 = 4050 24x + x2 = 4050 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 4050 + 144 Reorder the terms: 144 + 24x + x2 = 4050 + 144 Combine like terms: 4050 + 144 = 4194 144 + 24x + x2 = 4194 Factor a perfect square on the left side: (x + 12)(x + 12) = 4194 Calculate the square root of the right side: 64.761099435 Break this problem into two subproblems by setting (x + 12) equal to 64.761099435 and -64.761099435.Subproblem 1
x + 12 = 64.761099435 Simplifying x + 12 = 64.761099435 Reorder the terms: 12 + x = 64.761099435 Solving 12 + x = 64.761099435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 64.761099435 + -12 Combine like terms: 12 + -12 = 0 0 + x = 64.761099435 + -12 x = 64.761099435 + -12 Combine like terms: 64.761099435 + -12 = 52.761099435 x = 52.761099435 Simplifying x = 52.761099435Subproblem 2
x + 12 = -64.761099435 Simplifying x + 12 = -64.761099435 Reorder the terms: 12 + x = -64.761099435 Solving 12 + x = -64.761099435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -64.761099435 + -12 Combine like terms: 12 + -12 = 0 0 + x = -64.761099435 + -12 x = -64.761099435 + -12 Combine like terms: -64.761099435 + -12 = -76.761099435 x = -76.761099435 Simplifying x = -76.761099435Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.761099435, -76.761099435}
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