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Simplifying 4x + 3 = 25x2 Reorder the terms: 3 + 4x = 25x2 Solving 3 + 4x = 25x2 Solving for variable 'x'. Combine like terms: 25x2 + -25x2 = 0 3 + 4x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -0.12 + -0.16x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -0.16x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -0.16x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -0.16x + x2 = 0 + 0.12 -0.16x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -0.16x + x2 = 0.12 The x term is -0.16x. Take half its coefficient (-0.08). Square it (0.0064) and add it to both sides. Add '0.0064' to each side of the equation. -0.16x + 0.0064 + x2 = 0.12 + 0.0064 Reorder the terms: 0.0064 + -0.16x + x2 = 0.12 + 0.0064 Combine like terms: 0.12 + 0.0064 = 0.1264 0.0064 + -0.16x + x2 = 0.1264 Factor a perfect square on the left side: (x + -0.08)(x + -0.08) = 0.1264 Calculate the square root of the right side: 0.355527777 Break this problem into two subproblems by setting (x + -0.08) equal to 0.355527777 and -0.355527777.Subproblem 1
x + -0.08 = 0.355527777 Simplifying x + -0.08 = 0.355527777 Reorder the terms: -0.08 + x = 0.355527777 Solving -0.08 + x = 0.355527777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08' to each side of the equation. -0.08 + 0.08 + x = 0.355527777 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + x = 0.355527777 + 0.08 x = 0.355527777 + 0.08 Combine like terms: 0.355527777 + 0.08 = 0.435527777 x = 0.435527777 Simplifying x = 0.435527777Subproblem 2
x + -0.08 = -0.355527777 Simplifying x + -0.08 = -0.355527777 Reorder the terms: -0.08 + x = -0.355527777 Solving -0.08 + x = -0.355527777 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08' to each side of the equation. -0.08 + 0.08 + x = -0.355527777 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + x = -0.355527777 + 0.08 x = -0.355527777 + 0.08 Combine like terms: -0.355527777 + 0.08 = -0.275527777 x = -0.275527777 Simplifying x = -0.275527777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.435527777, -0.275527777}
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