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Simplifying 100x2 + 60x + 9 = 28 Reorder the terms: 9 + 60x + 100x2 = 28 Solving 9 + 60x + 100x2 = 28 Solving for variable 'x'. Reorder the terms: 9 + -28 + 60x + 100x2 = 28 + -28 Combine like terms: 9 + -28 = -19 -19 + 60x + 100x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -19 + 60x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.19 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.19' to each side of the equation. -0.19 + 0.6x + 0.19 + x2 = 0 + 0.19 Reorder the terms: -0.19 + 0.19 + 0.6x + x2 = 0 + 0.19 Combine like terms: -0.19 + 0.19 = 0.00 0.00 + 0.6x + x2 = 0 + 0.19 0.6x + x2 = 0 + 0.19 Combine like terms: 0 + 0.19 = 0.19 0.6x + x2 = 0.19 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 0.19 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.19 + 0.09 Combine like terms: 0.19 + 0.09 = 0.28 0.09 + 0.6x + x2 = 0.28 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.28 Calculate the square root of the right side: 0.529150262 Break this problem into two subproblems by setting (x + 0.3) equal to 0.529150262 and -0.529150262.Subproblem 1
x + 0.3 = 0.529150262 Simplifying x + 0.3 = 0.529150262 Reorder the terms: 0.3 + x = 0.529150262 Solving 0.3 + x = 0.529150262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 0.529150262 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.529150262 + -0.3 x = 0.529150262 + -0.3 Combine like terms: 0.529150262 + -0.3 = 0.229150262 x = 0.229150262 Simplifying x = 0.229150262Subproblem 2
x + 0.3 = -0.529150262 Simplifying x + 0.3 = -0.529150262 Reorder the terms: 0.3 + x = -0.529150262 Solving 0.3 + x = -0.529150262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -0.529150262 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.529150262 + -0.3 x = -0.529150262 + -0.3 Combine like terms: -0.529150262 + -0.3 = -0.829150262 x = -0.829150262 Simplifying x = -0.829150262Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.229150262, -0.829150262}
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