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Simplifying 74 = 25x2 + -5x Reorder the terms: 74 = -5x + 25x2 Solving 74 = -5x + 25x2 Solving for variable 'x'. Reorder the terms: 74 + 5x + -25x2 = -5x + 5x + 25x2 + -25x2 Combine like terms: -5x + 5x = 0 74 + 5x + -25x2 = 0 + 25x2 + -25x2 74 + 5x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 74 + 5x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -2.96 + -0.2x + x2 = 0 Move the constant term to the right: Add '2.96' to each side of the equation. -2.96 + -0.2x + 2.96 + x2 = 0 + 2.96 Reorder the terms: -2.96 + 2.96 + -0.2x + x2 = 0 + 2.96 Combine like terms: -2.96 + 2.96 = 0.00 0.00 + -0.2x + x2 = 0 + 2.96 -0.2x + x2 = 0 + 2.96 Combine like terms: 0 + 2.96 = 2.96 -0.2x + x2 = 2.96 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 2.96 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 2.96 + 0.01 Combine like terms: 2.96 + 0.01 = 2.97 0.01 + -0.2x + x2 = 2.97 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 2.97 Calculate the square root of the right side: 1.723368794 Break this problem into two subproblems by setting (x + -0.1) equal to 1.723368794 and -1.723368794.Subproblem 1
x + -0.1 = 1.723368794 Simplifying x + -0.1 = 1.723368794 Reorder the terms: -0.1 + x = 1.723368794 Solving -0.1 + x = 1.723368794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.723368794 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.723368794 + 0.1 x = 1.723368794 + 0.1 Combine like terms: 1.723368794 + 0.1 = 1.823368794 x = 1.823368794 Simplifying x = 1.823368794Subproblem 2
x + -0.1 = -1.723368794 Simplifying x + -0.1 = -1.723368794 Reorder the terms: -0.1 + x = -1.723368794 Solving -0.1 + x = -1.723368794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.723368794 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.723368794 + 0.1 x = -1.723368794 + 0.1 Combine like terms: -1.723368794 + 0.1 = -1.623368794 x = -1.623368794 Simplifying x = -1.623368794Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.823368794, -1.623368794}
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