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Simplifying 0 = x(x) + -4.75x + 3 Multiply x * x 0 = x2 + -4.75x + 3 Reorder the terms: 0 = 3 + -4.75x + x2 Solving 0 = 3 + -4.75x + x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 4.75x + -1x2 = 3 + -4.75x + x2 + -3 + 4.75x + -1x2 Reorder the terms: -3 + 4.75x + -1x2 = 3 + -3 + -4.75x + 4.75x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -3 + 4.75x + -1x2 = 0 + -4.75x + 4.75x + x2 + -1x2 -3 + 4.75x + -1x2 = -4.75x + 4.75x + x2 + -1x2 Combine like terms: -4.75x + 4.75x = 0.00 -3 + 4.75x + -1x2 = 0.00 + x2 + -1x2 -3 + 4.75x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3 + 4.75x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -4.75x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.75x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.75x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.75x + x2 = 0 + -3 -4.75x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.75x + x2 = -3 The x term is -4.75x. Take half its coefficient (-2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. -4.75x + 5.640625 + x2 = -3 + 5.640625 Reorder the terms: 5.640625 + -4.75x + x2 = -3 + 5.640625 Combine like terms: -3 + 5.640625 = 2.640625 5.640625 + -4.75x + x2 = 2.640625 Factor a perfect square on the left side: (x + -2.375)(x + -2.375) = 2.640625 Calculate the square root of the right side: 1.625 Break this problem into two subproblems by setting (x + -2.375) equal to 1.625 and -1.625.Subproblem 1
x + -2.375 = 1.625 Simplifying x + -2.375 = 1.625 Reorder the terms: -2.375 + x = 1.625 Solving -2.375 + x = 1.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 1.625 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 1.625 + 2.375 x = 1.625 + 2.375 Combine like terms: 1.625 + 2.375 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -2.375 = -1.625 Simplifying x + -2.375 = -1.625 Reorder the terms: -2.375 + x = -1.625 Solving -2.375 + x = -1.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -1.625 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -1.625 + 2.375 x = -1.625 + 2.375 Combine like terms: -1.625 + 2.375 = 0.75 x = 0.75 Simplifying x = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 0.75}
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