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Simplifying 50x2 + -10 = 7x + 75 Reorder the terms: -10 + 50x2 = 7x + 75 Reorder the terms: -10 + 50x2 = 75 + 7x Solving -10 + 50x2 = 75 + 7x Solving for variable 'x'. Reorder the terms: -10 + -75 + -7x + 50x2 = 75 + 7x + -75 + -7x Combine like terms: -10 + -75 = -85 -85 + -7x + 50x2 = 75 + 7x + -75 + -7x Reorder the terms: -85 + -7x + 50x2 = 75 + -75 + 7x + -7x Combine like terms: 75 + -75 = 0 -85 + -7x + 50x2 = 0 + 7x + -7x -85 + -7x + 50x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -85 + -7x + 50x2 = 0 Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -1.7 + -0.14x + x2 = 0 Move the constant term to the right: Add '1.7' to each side of the equation. -1.7 + -0.14x + 1.7 + x2 = 0 + 1.7 Reorder the terms: -1.7 + 1.7 + -0.14x + x2 = 0 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + -0.14x + x2 = 0 + 1.7 -0.14x + x2 = 0 + 1.7 Combine like terms: 0 + 1.7 = 1.7 -0.14x + x2 = 1.7 The x term is -0.14x. Take half its coefficient (-0.07). Square it (0.0049) and add it to both sides. Add '0.0049' to each side of the equation. -0.14x + 0.0049 + x2 = 1.7 + 0.0049 Reorder the terms: 0.0049 + -0.14x + x2 = 1.7 + 0.0049 Combine like terms: 1.7 + 0.0049 = 1.7049 0.0049 + -0.14x + x2 = 1.7049 Factor a perfect square on the left side: (x + -0.07)(x + -0.07) = 1.7049 Calculate the square root of the right side: 1.305718193 Break this problem into two subproblems by setting (x + -0.07) equal to 1.305718193 and -1.305718193.Subproblem 1
x + -0.07 = 1.305718193 Simplifying x + -0.07 = 1.305718193 Reorder the terms: -0.07 + x = 1.305718193 Solving -0.07 + x = 1.305718193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07' to each side of the equation. -0.07 + 0.07 + x = 1.305718193 + 0.07 Combine like terms: -0.07 + 0.07 = 0.00 0.00 + x = 1.305718193 + 0.07 x = 1.305718193 + 0.07 Combine like terms: 1.305718193 + 0.07 = 1.375718193 x = 1.375718193 Simplifying x = 1.375718193Subproblem 2
x + -0.07 = -1.305718193 Simplifying x + -0.07 = -1.305718193 Reorder the terms: -0.07 + x = -1.305718193 Solving -0.07 + x = -1.305718193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07' to each side of the equation. -0.07 + 0.07 + x = -1.305718193 + 0.07 Combine like terms: -0.07 + 0.07 = 0.00 0.00 + x = -1.305718193 + 0.07 x = -1.305718193 + 0.07 Combine like terms: -1.305718193 + 0.07 = -1.235718193 x = -1.235718193 Simplifying x = -1.235718193Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.375718193, -1.235718193}
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