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Simplifying 5x2 + -10.5x + 2.16 = 0 Reorder the terms: 2.16 + -10.5x + 5x2 = 0 Solving 2.16 + -10.5x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.432 + -2.1x + x2 = 0 Move the constant term to the right: Add '-0.432' to each side of the equation. 0.432 + -2.1x + -0.432 + x2 = 0 + -0.432 Reorder the terms: 0.432 + -0.432 + -2.1x + x2 = 0 + -0.432 Combine like terms: 0.432 + -0.432 = 0.000 0.000 + -2.1x + x2 = 0 + -0.432 -2.1x + x2 = 0 + -0.432 Combine like terms: 0 + -0.432 = -0.432 -2.1x + x2 = -0.432 The x term is -2.1x. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1x + 1.1025 + x2 = -0.432 + 1.1025 Reorder the terms: 1.1025 + -2.1x + x2 = -0.432 + 1.1025 Combine like terms: -0.432 + 1.1025 = 0.6705 1.1025 + -2.1x + x2 = 0.6705 Factor a perfect square on the left side: (x + -1.05)(x + -1.05) = 0.6705 Calculate the square root of the right side: 0.818840644 Break this problem into two subproblems by setting (x + -1.05) equal to 0.818840644 and -0.818840644.Subproblem 1
x + -1.05 = 0.818840644 Simplifying x + -1.05 = 0.818840644 Reorder the terms: -1.05 + x = 0.818840644 Solving -1.05 + x = 0.818840644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = 0.818840644 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 0.818840644 + 1.05 x = 0.818840644 + 1.05 Combine like terms: 0.818840644 + 1.05 = 1.868840644 x = 1.868840644 Simplifying x = 1.868840644Subproblem 2
x + -1.05 = -0.818840644 Simplifying x + -1.05 = -0.818840644 Reorder the terms: -1.05 + x = -0.818840644 Solving -1.05 + x = -0.818840644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = -0.818840644 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -0.818840644 + 1.05 x = -0.818840644 + 1.05 Combine like terms: -0.818840644 + 1.05 = 0.231159356 x = 0.231159356 Simplifying x = 0.231159356Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.868840644, 0.231159356}
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