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Simplifying 5x2 + 3 = 10x Reorder the terms: 3 + 5x2 = 10x Solving 3 + 5x2 = 10x Solving for variable 'x'. Reorder the terms: 3 + -10x + 5x2 = 10x + -10x Combine like terms: 10x + -10x = 0 3 + -10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -2x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -2x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -2x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -2x + x2 = 0 + -0.6 -2x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -2x + x2 = -0.6 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.6 + 1 Reorder the terms: 1 + -2x + x2 = -0.6 + 1 Combine like terms: -0.6 + 1 = 0.4 1 + -2x + x2 = 0.4 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.4 Calculate the square root of the right side: 0.632455532 Break this problem into two subproblems by setting (x + -1) equal to 0.632455532 and -0.632455532.Subproblem 1
x + -1 = 0.632455532 Simplifying x + -1 = 0.632455532 Reorder the terms: -1 + x = 0.632455532 Solving -1 + x = 0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.632455532 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.632455532 + 1 x = 0.632455532 + 1 Combine like terms: 0.632455532 + 1 = 1.632455532 x = 1.632455532 Simplifying x = 1.632455532Subproblem 2
x + -1 = -0.632455532 Simplifying x + -1 = -0.632455532 Reorder the terms: -1 + x = -0.632455532 Solving -1 + x = -0.632455532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.632455532 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.632455532 + 1 x = -0.632455532 + 1 Combine like terms: -0.632455532 + 1 = 0.367544468 x = 0.367544468 Simplifying x = 0.367544468Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.632455532, 0.367544468}
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