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Simplifying 4x + 73x(2x) = 43 Remove parenthesis around (2x) 4x + 73x * 2x = 43 Reorder the terms for easier multiplication: 4x + 73 * 2x * x = 43 Multiply 73 * 2 4x + 146x * x = 43 Multiply x * x 4x + 146x2 = 43 Solving 4x + 146x2 = 43 Solving for variable 'x'. Reorder the terms: -43 + 4x + 146x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + 4x + 146x2 = 0 Begin completing the square. Divide all terms by 146 the coefficient of the squared term: Divide each side by '146'. -0.2945205479 + 0.02739726027x + x2 = 0 Move the constant term to the right: Add '0.2945205479' to each side of the equation. -0.2945205479 + 0.02739726027x + 0.2945205479 + x2 = 0 + 0.2945205479 Reorder the terms: -0.2945205479 + 0.2945205479 + 0.02739726027x + x2 = 0 + 0.2945205479 Combine like terms: -0.2945205479 + 0.2945205479 = 0.0000000000 0.0000000000 + 0.02739726027x + x2 = 0 + 0.2945205479 0.02739726027x + x2 = 0 + 0.2945205479 Combine like terms: 0 + 0.2945205479 = 0.2945205479 0.02739726027x + x2 = 0.2945205479 The x term is 0.02739726027x. Take half its coefficient (0.01369863014). Square it (0.0001876524677) and add it to both sides. Add '0.0001876524677' to each side of the equation. 0.02739726027x + 0.0001876524677 + x2 = 0.2945205479 + 0.0001876524677 Reorder the terms: 0.0001876524677 + 0.02739726027x + x2 = 0.2945205479 + 0.0001876524677 Combine like terms: 0.2945205479 + 0.0001876524677 = 0.2947082003677 0.0001876524677 + 0.02739726027x + x2 = 0.2947082003677 Factor a perfect square on the left side: (x + 0.01369863014)(x + 0.01369863014) = 0.2947082003677 Calculate the square root of the right side: 0.542870335 Break this problem into two subproblems by setting (x + 0.01369863014) equal to 0.542870335 and -0.542870335.Subproblem 1
x + 0.01369863014 = 0.542870335 Simplifying x + 0.01369863014 = 0.542870335 Reorder the terms: 0.01369863014 + x = 0.542870335 Solving 0.01369863014 + x = 0.542870335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01369863014' to each side of the equation. 0.01369863014 + -0.01369863014 + x = 0.542870335 + -0.01369863014 Combine like terms: 0.01369863014 + -0.01369863014 = 0.00000000000 0.00000000000 + x = 0.542870335 + -0.01369863014 x = 0.542870335 + -0.01369863014 Combine like terms: 0.542870335 + -0.01369863014 = 0.52917170486 x = 0.52917170486 Simplifying x = 0.52917170486Subproblem 2
x + 0.01369863014 = -0.542870335 Simplifying x + 0.01369863014 = -0.542870335 Reorder the terms: 0.01369863014 + x = -0.542870335 Solving 0.01369863014 + x = -0.542870335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01369863014' to each side of the equation. 0.01369863014 + -0.01369863014 + x = -0.542870335 + -0.01369863014 Combine like terms: 0.01369863014 + -0.01369863014 = 0.00000000000 0.00000000000 + x = -0.542870335 + -0.01369863014 x = -0.542870335 + -0.01369863014 Combine like terms: -0.542870335 + -0.01369863014 = -0.55656896514 x = -0.55656896514 Simplifying x = -0.55656896514Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.52917170486, -0.55656896514}
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