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Simplifying 25x2 + 3x + -4 = 5 Reorder the terms: -4 + 3x + 25x2 = 5 Solving -4 + 3x + 25x2 = 5 Solving for variable 'x'. Reorder the terms: -4 + -5 + 3x + 25x2 = 5 + -5 Combine like terms: -4 + -5 = -9 -9 + 3x + 25x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -9 + 3x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.36 + 0.12x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + 0.12x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + 0.12x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + 0.12x + x2 = 0 + 0.36 0.12x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 0.12x + x2 = 0.36 The x term is 0.12x. Take half its coefficient (0.06). Square it (0.0036) and add it to both sides. Add '0.0036' to each side of the equation. 0.12x + 0.0036 + x2 = 0.36 + 0.0036 Reorder the terms: 0.0036 + 0.12x + x2 = 0.36 + 0.0036 Combine like terms: 0.36 + 0.0036 = 0.3636 0.0036 + 0.12x + x2 = 0.3636 Factor a perfect square on the left side: (x + 0.06)(x + 0.06) = 0.3636 Calculate the square root of the right side: 0.602992537 Break this problem into two subproblems by setting (x + 0.06) equal to 0.602992537 and -0.602992537.Subproblem 1
x + 0.06 = 0.602992537 Simplifying x + 0.06 = 0.602992537 Reorder the terms: 0.06 + x = 0.602992537 Solving 0.06 + x = 0.602992537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = 0.602992537 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = 0.602992537 + -0.06 x = 0.602992537 + -0.06 Combine like terms: 0.602992537 + -0.06 = 0.542992537 x = 0.542992537 Simplifying x = 0.542992537Subproblem 2
x + 0.06 = -0.602992537 Simplifying x + 0.06 = -0.602992537 Reorder the terms: 0.06 + x = -0.602992537 Solving 0.06 + x = -0.602992537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06' to each side of the equation. 0.06 + -0.06 + x = -0.602992537 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 0.00 + x = -0.602992537 + -0.06 x = -0.602992537 + -0.06 Combine like terms: -0.602992537 + -0.06 = -0.662992537 x = -0.662992537 Simplifying x = -0.662992537Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.542992537, -0.662992537}
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