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Simplifying 4x2 + 0.84x = 0.525 Reorder the terms: 0.84x + 4x2 = 0.525 Solving 0.84x + 4x2 = 0.525 Solving for variable 'x'. Reorder the terms: -0.525 + 0.84x + 4x2 = 0.525 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 -0.525 + 0.84x + 4x2 = 0.000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.13125 + 0.21x + x2 = 0.000 Move the constant term to the right: Add '0.13125' to each side of the equation. -0.13125 + 0.21x + 0.13125 + x2 = 0.000 + 0.13125 Reorder the terms: -0.13125 + 0.13125 + 0.21x + x2 = 0.000 + 0.13125 Combine like terms: -0.13125 + 0.13125 = 0.00000 0.00000 + 0.21x + x2 = 0.000 + 0.13125 0.21x + x2 = 0.000 + 0.13125 Combine like terms: 0.000 + 0.13125 = 0.13125 0.21x + x2 = 0.13125 The x term is 0.21x. Take half its coefficient (0.105). Square it (0.011025) and add it to both sides. Add '0.011025' to each side of the equation. 0.21x + 0.011025 + x2 = 0.13125 + 0.011025 Reorder the terms: 0.011025 + 0.21x + x2 = 0.13125 + 0.011025 Combine like terms: 0.13125 + 0.011025 = 0.142275 0.011025 + 0.21x + x2 = 0.142275 Factor a perfect square on the left side: (x + 0.105)(x + 0.105) = 0.142275 Calculate the square root of the right side: 0.377193584 Break this problem into two subproblems by setting (x + 0.105) equal to 0.377193584 and -0.377193584.Subproblem 1
x + 0.105 = 0.377193584 Simplifying x + 0.105 = 0.377193584 Reorder the terms: 0.105 + x = 0.377193584 Solving 0.105 + x = 0.377193584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.105' to each side of the equation. 0.105 + -0.105 + x = 0.377193584 + -0.105 Combine like terms: 0.105 + -0.105 = 0.000 0.000 + x = 0.377193584 + -0.105 x = 0.377193584 + -0.105 Combine like terms: 0.377193584 + -0.105 = 0.272193584 x = 0.272193584 Simplifying x = 0.272193584Subproblem 2
x + 0.105 = -0.377193584 Simplifying x + 0.105 = -0.377193584 Reorder the terms: 0.105 + x = -0.377193584 Solving 0.105 + x = -0.377193584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.105' to each side of the equation. 0.105 + -0.105 + x = -0.377193584 + -0.105 Combine like terms: 0.105 + -0.105 = 0.000 0.000 + x = -0.377193584 + -0.105 x = -0.377193584 + -0.105 Combine like terms: -0.377193584 + -0.105 = -0.482193584 x = -0.482193584 Simplifying x = -0.482193584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.272193584, -0.482193584}
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